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Simplifying t(t + -15) = 70 Reorder the terms: t(-15 + t) = 70 (-15 * t + t * t) = 70 (-15t + t2) = 70 Solving -15t + t2 = 70 Solving for variable 't'. Reorder the terms: -70 + -15t + t2 = 70 + -70 Combine like terms: 70 + -70 = 0 -70 + -15t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + -15t + 70 + t2 = 0 + 70 Reorder the terms: -70 + 70 + -15t + t2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -15t + t2 = 0 + 70 -15t + t2 = 0 + 70 Combine like terms: 0 + 70 = 70 -15t + t2 = 70 The t term is -15t. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15t + 56.25 + t2 = 70 + 56.25 Reorder the terms: 56.25 + -15t + t2 = 70 + 56.25 Combine like terms: 70 + 56.25 = 126.25 56.25 + -15t + t2 = 126.25 Factor a perfect square on the left side: (t + -7.5)(t + -7.5) = 126.25 Calculate the square root of the right side: 11.236102527 Break this problem into two subproblems by setting (t + -7.5) equal to 11.236102527 and -11.236102527.Subproblem 1
t + -7.5 = 11.236102527 Simplifying t + -7.5 = 11.236102527 Reorder the terms: -7.5 + t = 11.236102527 Solving -7.5 + t = 11.236102527 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + t = 11.236102527 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + t = 11.236102527 + 7.5 t = 11.236102527 + 7.5 Combine like terms: 11.236102527 + 7.5 = 18.736102527 t = 18.736102527 Simplifying t = 18.736102527Subproblem 2
t + -7.5 = -11.236102527 Simplifying t + -7.5 = -11.236102527 Reorder the terms: -7.5 + t = -11.236102527 Solving -7.5 + t = -11.236102527 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + t = -11.236102527 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + t = -11.236102527 + 7.5 t = -11.236102527 + 7.5 Combine like terms: -11.236102527 + 7.5 = -3.736102527 t = -3.736102527 Simplifying t = -3.736102527Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.736102527, -3.736102527}
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