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Simplifying 70t2 + 140t + -50 = 0 Reorder the terms: -50 + 140t + 70t2 = 0 Solving -50 + 140t + 70t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '10'. 10(-5 + 14t + 7t2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-5 + 14t + 7t2)' equal to zero and attempt to solve: Simplifying -5 + 14t + 7t2 = 0 Solving -5 + 14t + 7t2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + 2t + t2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 2t + 0.7142857143 + t2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 2t + t2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 2t + t2 = 0 + 0.7142857143 2t + t2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 2t + t2 = 0.7142857143 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = 0.7142857143 + 1 Reorder the terms: 1 + 2t + t2 = 0.7142857143 + 1 Combine like terms: 0.7142857143 + 1 = 1.7142857143 1 + 2t + t2 = 1.7142857143 Factor a perfect square on the left side: (t + 1)(t + 1) = 1.7142857143 Calculate the square root of the right side: 1.309307341 Break this problem into two subproblems by setting (t + 1) equal to 1.309307341 and -1.309307341.Subproblem 1
t + 1 = 1.309307341 Simplifying t + 1 = 1.309307341 Reorder the terms: 1 + t = 1.309307341 Solving 1 + t = 1.309307341 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 1.309307341 + -1 Combine like terms: 1 + -1 = 0 0 + t = 1.309307341 + -1 t = 1.309307341 + -1 Combine like terms: 1.309307341 + -1 = 0.309307341 t = 0.309307341 Simplifying t = 0.309307341Subproblem 2
t + 1 = -1.309307341 Simplifying t + 1 = -1.309307341 Reorder the terms: 1 + t = -1.309307341 Solving 1 + t = -1.309307341 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -1.309307341 + -1 Combine like terms: 1 + -1 = 0 0 + t = -1.309307341 + -1 t = -1.309307341 + -1 Combine like terms: -1.309307341 + -1 = -2.309307341 t = -2.309307341 Simplifying t = -2.309307341Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.309307341, -2.309307341}Solution
t = {0.309307341, -2.309307341}
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