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Simplifying 4590 = 40t4 + 1560t2 Reorder the terms: 4590 = 1560t2 + 40t4 Solving 4590 = 1560t2 + 40t4 Solving for variable 't'. Reorder the terms: 4590 + -1560t2 + -40t4 = 1560t2 + -1560t2 + 40t4 + -40t4 Combine like terms: 1560t2 + -1560t2 = 0 4590 + -1560t2 + -40t4 = 0 + 40t4 + -40t4 4590 + -1560t2 + -40t4 = 40t4 + -40t4 Combine like terms: 40t4 + -40t4 = 0 4590 + -1560t2 + -40t4 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(459 + -156t2 + -4t4) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(459 + -156t2 + -4t4)' equal to zero and attempt to solve: Simplifying 459 + -156t2 + -4t4 = 0 Solving 459 + -156t2 + -4t4 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -114.75 + 39t2 + t4 = 0 Move the constant term to the right: Add '114.75' to each side of the equation. -114.75 + 39t2 + 114.75 + t4 = 0 + 114.75 Reorder the terms: -114.75 + 114.75 + 39t2 + t4 = 0 + 114.75 Combine like terms: -114.75 + 114.75 = 0.00 0.00 + 39t2 + t4 = 0 + 114.75 39t2 + t4 = 0 + 114.75 Combine like terms: 0 + 114.75 = 114.75 39t2 + t4 = 114.75 The t term is 39t2. Take half its coefficient (19.5). Square it (380.25) and add it to both sides. Add '380.25' to each side of the equation. 39t2 + 380.25 + t4 = 114.75 + 380.25 Reorder the terms: 380.25 + 39t2 + t4 = 114.75 + 380.25 Combine like terms: 114.75 + 380.25 = 495 380.25 + 39t2 + t4 = 495 Factor a perfect square on the left side: (t2 + 19.5)(t2 + 19.5) = 495 Calculate the square root of the right side: 22.248595461 Break this problem into two subproblems by setting (t2 + 19.5) equal to 22.248595461 and -22.248595461.Subproblem 1
t2 + 19.5 = 22.248595461 Simplifying t2 + 19.5 = 22.248595461 Reorder the terms: 19.5 + t2 = 22.248595461 Solving 19.5 + t2 = 22.248595461 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + t2 = 22.248595461 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + t2 = 22.248595461 + -19.5 t2 = 22.248595461 + -19.5 Combine like terms: 22.248595461 + -19.5 = 2.748595461 t2 = 2.748595461 Simplifying t2 = 2.748595461 Take the square root of each side: t = {-1.657888857, 1.657888857}Subproblem 2
t2 + 19.5 = -22.248595461 Simplifying t2 + 19.5 = -22.248595461 Reorder the terms: 19.5 + t2 = -22.248595461 Solving 19.5 + t2 = -22.248595461 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + t2 = -22.248595461 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + t2 = -22.248595461 + -19.5 t2 = -22.248595461 + -19.5 Combine like terms: -22.248595461 + -19.5 = -41.748595461 t2 = -41.748595461 Simplifying t2 = -41.748595461 Reorder the terms: 41.748595461 + t2 = -41.748595461 + 41.748595461 Combine like terms: -41.748595461 + 41.748595461 = 0.000000000 41.748595461 + t2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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