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Simplifying (12t2 + t)(12t2 + t) + -14(12T2 + t) + 13 = 0 Reorder the terms: (t + 12t2)(12t2 + t) + -14(12T2 + t) + 13 = 0 Reorder the terms: (t + 12t2)(t + 12t2) + -14(12T2 + t) + 13 = 0 Multiply (t + 12t2) * (t + 12t2) (t(t + 12t2) + 12t2 * (t + 12t2)) + -14(12T2 + t) + 13 = 0 ((t * t + 12t2 * t) + 12t2 * (t + 12t2)) + -14(12T2 + t) + 13 = 0 ((t2 + 12t3) + 12t2 * (t + 12t2)) + -14(12T2 + t) + 13 = 0 (t2 + 12t3 + (t * 12t2 + 12t2 * 12t2)) + -14(12T2 + t) + 13 = 0 (t2 + 12t3 + (12t3 + 144t4)) + -14(12T2 + t) + 13 = 0 Combine like terms: 12t3 + 12t3 = 24t3 (t2 + 24t3 + 144t4) + -14(12T2 + t) + 13 = 0 t2 + 24t3 + 144t4 + (12T2 * -14 + t * -14) + 13 = 0 t2 + 24t3 + 144t4 + (-168T2 + -14t) + 13 = 0 Reorder the terms: 13 + -168T2 + -14t + t2 + 24t3 + 144t4 = 0 Solving 13 + -168T2 + -14t + t2 + 24t3 + 144t4 = 0 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -168T2 + -14t + t2 + 24t3 + -13 + 144t4 = 0 + -13 Reorder the terms: 13 + -13 + -168T2 + -14t + t2 + 24t3 + 144t4 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -168T2 + -14t + t2 + 24t3 + 144t4 = 0 + -13 -168T2 + -14t + t2 + 24t3 + 144t4 = 0 + -13 Combine like terms: 0 + -13 = -13 -168T2 + -14t + t2 + 24t3 + 144t4 = -13 Add '14t' to each side of the equation. -168T2 + -14t + t2 + 24t3 + 14t + 144t4 = -13 + 14t Reorder the terms: -168T2 + -14t + 14t + t2 + 24t3 + 144t4 = -13 + 14t Combine like terms: -14t + 14t = 0 -168T2 + 0 + t2 + 24t3 + 144t4 = -13 + 14t -168T2 + t2 + 24t3 + 144t4 = -13 + 14t Add '-1t2' to each side of the equation. -168T2 + t2 + 24t3 + -1t2 + 144t4 = -13 + 14t + -1t2 Reorder the terms: -168T2 + t2 + -1t2 + 24t3 + 144t4 = -13 + 14t + -1t2 Combine like terms: t2 + -1t2 = 0 -168T2 + 0 + 24t3 + 144t4 = -13 + 14t + -1t2 -168T2 + 24t3 + 144t4 = -13 + 14t + -1t2 Add '-24t3' to each side of the equation. -168T2 + 24t3 + -24t3 + 144t4 = -13 + 14t + -1t2 + -24t3 Combine like terms: 24t3 + -24t3 = 0 -168T2 + 0 + 144t4 = -13 + 14t + -1t2 + -24t3 -168T2 + 144t4 = -13 + 14t + -1t2 + -24t3 Add '-144t4' to each side of the equation. -168T2 + 144t4 + -144t4 = -13 + 14t + -1t2 + -24t3 + -144t4 Combine like terms: 144t4 + -144t4 = 0 -168T2 + 0 = -13 + 14t + -1t2 + -24t3 + -144t4 -168T2 = -13 + 14t + -1t2 + -24t3 + -144t4 Divide each side by '-168'. T2 = 0.07738095238 + -0.08333333333t + 0.005952380952t2 + 0.1428571429t3 + 0.8571428571t4 Simplifying T2 = 0.07738095238 + -0.08333333333t + 0.005952380952t2 + 0.1428571429t3 + 0.8571428571t4 Reorder the terms: -0.07738095238 + T2 + 0.08333333333t + -0.005952380952t2 + -0.1428571429t3 + -0.8571428571t4 = 0.07738095238 + -0.08333333333t + 0.005952380952t2 + 0.1428571429t3 + 0.8571428571t4 + -0.07738095238 + 0.08333333333t + -0.005952380952t2 + -0.1428571429t3 + -0.8571428571t4 Reorder the terms: -0.07738095238 + T2 + 0.08333333333t + -0.005952380952t2 + -0.1428571429t3 + -0.8571428571t4 = 0.07738095238 + -0.07738095238 + -0.08333333333t + 0.08333333333t + 0.005952380952t2 + -0.005952380952t2 + 0.1428571429t3 + -0.1428571429t3 + 0.8571428571t4 + -0.8571428571t4 Combine like terms: 0.07738095238 + -0.07738095238 = 0.00000000000 -0.07738095238 + T2 + 0.08333333333t + -0.005952380952t2 + -0.1428571429t3 + -0.8571428571t4 = 0.00000000000 + -0.08333333333t + 0.08333333333t + 0.005952380952t2 + -0.005952380952t2 + 0.1428571429t3 + -0.1428571429t3 + 0.8571428571t4 + -0.8571428571t4 -0.07738095238 + T2 + 0.08333333333t + -0.005952380952t2 + -0.1428571429t3 + -0.8571428571t4 = -0.08333333333t + 0.08333333333t + 0.005952380952t2 + -0.005952380952t2 + 0.1428571429t3 + -0.1428571429t3 + 0.8571428571t4 + -0.8571428571t4 Combine like terms: -0.08333333333t + 0.08333333333t = 0.00000000000 -0.07738095238 + T2 + 0.08333333333t + -0.005952380952t2 + -0.1428571429t3 + -0.8571428571t4 = 0.00000000000 + 0.005952380952t2 + -0.005952380952t2 + 0.1428571429t3 + -0.1428571429t3 + 0.8571428571t4 + -0.8571428571t4 -0.07738095238 + T2 + 0.08333333333t + -0.005952380952t2 + -0.1428571429t3 + -0.8571428571t4 = 0.005952380952t2 + -0.005952380952t2 + 0.1428571429t3 + -0.1428571429t3 + 0.8571428571t4 + -0.8571428571t4 Combine like terms: 0.005952380952t2 + -0.005952380952t2 = 0.000000000000 -0.07738095238 + T2 + 0.08333333333t + -0.005952380952t2 + -0.1428571429t3 + -0.8571428571t4 = 0.000000000000 + 0.1428571429t3 + -0.1428571429t3 + 0.8571428571t4 + -0.8571428571t4 -0.07738095238 + T2 + 0.08333333333t + -0.005952380952t2 + -0.1428571429t3 + -0.8571428571t4 = 0.1428571429t3 + -0.1428571429t3 + 0.8571428571t4 + -0.8571428571t4 Combine like terms: 0.1428571429t3 + -0.1428571429t3 = 0.0000000000 -0.07738095238 + T2 + 0.08333333333t + -0.005952380952t2 + -0.1428571429t3 + -0.8571428571t4 = 0.0000000000 + 0.8571428571t4 + -0.8571428571t4 -0.07738095238 + T2 + 0.08333333333t + -0.005952380952t2 + -0.1428571429t3 + -0.8571428571t4 = 0.8571428571t4 + -0.8571428571t4 Combine like terms: 0.8571428571t4 + -0.8571428571t4 = 0.0000000000 -0.07738095238 + T2 + 0.08333333333t + -0.005952380952t2 + -0.1428571429t3 + -0.8571428571t4 = 0.0000000000 The solution to this equation could not be determined.
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