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Simplifying t = -16t2 + 70t + 4 Reorder the terms: t = 4 + 70t + -16t2 Solving t = 4 + 70t + -16t2 Solving for variable 't'. Reorder the terms: -4 + t + -70t + 16t2 = 4 + 70t + -16t2 + -4 + -70t + 16t2 Combine like terms: t + -70t = -69t -4 + -69t + 16t2 = 4 + 70t + -16t2 + -4 + -70t + 16t2 Reorder the terms: -4 + -69t + 16t2 = 4 + -4 + 70t + -70t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 -4 + -69t + 16t2 = 0 + 70t + -70t + -16t2 + 16t2 -4 + -69t + 16t2 = 70t + -70t + -16t2 + 16t2 Combine like terms: 70t + -70t = 0 -4 + -69t + 16t2 = 0 + -16t2 + 16t2 -4 + -69t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -4 + -69t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.25 + -4.3125t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -4.3125t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -4.3125t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -4.3125t + t2 = 0 + 0.25 -4.3125t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -4.3125t + t2 = 0.25 The t term is -4.3125t. Take half its coefficient (-2.15625). Square it (4.649414063) and add it to both sides. Add '4.649414063' to each side of the equation. -4.3125t + 4.649414063 + t2 = 0.25 + 4.649414063 Reorder the terms: 4.649414063 + -4.3125t + t2 = 0.25 + 4.649414063 Combine like terms: 0.25 + 4.649414063 = 4.899414063 4.649414063 + -4.3125t + t2 = 4.899414063 Factor a perfect square on the left side: (t + -2.15625)(t + -2.15625) = 4.899414063 Calculate the square root of the right side: 2.213462008 Break this problem into two subproblems by setting (t + -2.15625) equal to 2.213462008 and -2.213462008.Subproblem 1
t + -2.15625 = 2.213462008 Simplifying t + -2.15625 = 2.213462008 Reorder the terms: -2.15625 + t = 2.213462008 Solving -2.15625 + t = 2.213462008 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.15625' to each side of the equation. -2.15625 + 2.15625 + t = 2.213462008 + 2.15625 Combine like terms: -2.15625 + 2.15625 = 0.00000 0.00000 + t = 2.213462008 + 2.15625 t = 2.213462008 + 2.15625 Combine like terms: 2.213462008 + 2.15625 = 4.369712008 t = 4.369712008 Simplifying t = 4.369712008Subproblem 2
t + -2.15625 = -2.213462008 Simplifying t + -2.15625 = -2.213462008 Reorder the terms: -2.15625 + t = -2.213462008 Solving -2.15625 + t = -2.213462008 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.15625' to each side of the equation. -2.15625 + 2.15625 + t = -2.213462008 + 2.15625 Combine like terms: -2.15625 + 2.15625 = 0.00000 0.00000 + t = -2.213462008 + 2.15625 t = -2.213462008 + 2.15625 Combine like terms: -2.213462008 + 2.15625 = -0.057212008 t = -0.057212008 Simplifying t = -0.057212008Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.369712008, -0.057212008}
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