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Simplifying 14t2 + -14t + 10 = 0 Reorder the terms: 10 + -14t + 14t2 = 0 Solving 10 + -14t + 14t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -7t + 7t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -7t + 7t2)' equal to zero and attempt to solve: Simplifying 5 + -7t + 7t2 = 0 Solving 5 + -7t + 7t2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.7142857143 + -1t + t2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + -1t + -0.7142857143 + t2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + -1t + t2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + -1t + t2 = 0 + -0.7142857143 -1t + t2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 -1t + t2 = -0.7142857143 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = -0.7142857143 + 0.25 Reorder the terms: 0.25 + -1t + t2 = -0.7142857143 + 0.25 Combine like terms: -0.7142857143 + 0.25 = -0.4642857143 0.25 + -1t + t2 = -0.4642857143 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = -0.4642857143 Can't calculate square root of the right side. 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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