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Simplifying -15t2 + 150t + -90 = 0 Reorder the terms: -90 + 150t + -15t2 = 0 Solving -90 + 150t + -15t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '15'. 15(-6 + 10t + -1t2) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-6 + 10t + -1t2)' equal to zero and attempt to solve: Simplifying -6 + 10t + -1t2 = 0 Solving -6 + 10t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6 + -10t + t2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -10t + -6 + t2 = 0 + -6 Reorder the terms: 6 + -6 + -10t + t2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -10t + t2 = 0 + -6 -10t + t2 = 0 + -6 Combine like terms: 0 + -6 = -6 -10t + t2 = -6 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = -6 + 25 Reorder the terms: 25 + -10t + t2 = -6 + 25 Combine like terms: -6 + 25 = 19 25 + -10t + t2 = 19 Factor a perfect square on the left side: (t + -5)(t + -5) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (t + -5) equal to 4.358898944 and -4.358898944.Subproblem 1
t + -5 = 4.358898944 Simplifying t + -5 = 4.358898944 Reorder the terms: -5 + t = 4.358898944 Solving -5 + t = 4.358898944 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 4.358898944 + 5 Combine like terms: -5 + 5 = 0 0 + t = 4.358898944 + 5 t = 4.358898944 + 5 Combine like terms: 4.358898944 + 5 = 9.358898944 t = 9.358898944 Simplifying t = 9.358898944Subproblem 2
t + -5 = -4.358898944 Simplifying t + -5 = -4.358898944 Reorder the terms: -5 + t = -4.358898944 Solving -5 + t = -4.358898944 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -4.358898944 + 5 Combine like terms: -5 + 5 = 0 0 + t = -4.358898944 + 5 t = -4.358898944 + 5 Combine like terms: -4.358898944 + 5 = 0.641101056 t = 0.641101056 Simplifying t = 0.641101056Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.358898944, 0.641101056}Solution
t = {9.358898944, 0.641101056}
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