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Simplifying 0(t) = -16t2 + 50t + 90 Anything times zero is zero. 0t = -16t2 + 50t + 90 Reorder the terms: 0 = 90 + 50t + -16t2 Solving 0 = 90 + 50t + -16t2 Solving for variable 't'. Combine like terms: 0 + -90 = -90 -90 + -50t + 16t2 = 90 + 50t + -16t2 + -90 + -50t + 16t2 Reorder the terms: -90 + -50t + 16t2 = 90 + -90 + 50t + -50t + -16t2 + 16t2 Combine like terms: 90 + -90 = 0 -90 + -50t + 16t2 = 0 + 50t + -50t + -16t2 + 16t2 -90 + -50t + 16t2 = 50t + -50t + -16t2 + 16t2 Combine like terms: 50t + -50t = 0 -90 + -50t + 16t2 = 0 + -16t2 + 16t2 -90 + -50t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -90 + -50t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + -25t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + -25t + 8t2)' equal to zero and attempt to solve: Simplifying -45 + -25t + 8t2 = 0 Solving -45 + -25t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.625 + -3.125t + t2 = 0 Move the constant term to the right: Add '5.625' to each side of the equation. -5.625 + -3.125t + 5.625 + t2 = 0 + 5.625 Reorder the terms: -5.625 + 5.625 + -3.125t + t2 = 0 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + -3.125t + t2 = 0 + 5.625 -3.125t + t2 = 0 + 5.625 Combine like terms: 0 + 5.625 = 5.625 -3.125t + t2 = 5.625 The t term is -3.125t. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125t + 2.44140625 + t2 = 5.625 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = 5.625 + 2.44140625 Combine like terms: 5.625 + 2.44140625 = 8.06640625 2.44140625 + -3.125t + t2 = 8.06640625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 8.06640625 Calculate the square root of the right side: 2.840141942 Break this problem into two subproblems by setting (t + -1.5625) equal to 2.840141942 and -2.840141942.Subproblem 1
t + -1.5625 = 2.840141942 Simplifying t + -1.5625 = 2.840141942 Reorder the terms: -1.5625 + t = 2.840141942 Solving -1.5625 + t = 2.840141942 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + t = 2.840141942 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 2.840141942 + 1.5625 t = 2.840141942 + 1.5625 Combine like terms: 2.840141942 + 1.5625 = 4.402641942 t = 4.402641942 Simplifying t = 4.402641942Subproblem 2
t + -1.5625 = -2.840141942 Simplifying t + -1.5625 = -2.840141942 Reorder the terms: -1.5625 + t = -2.840141942 Solving -1.5625 + t = -2.840141942 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + t = -2.840141942 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -2.840141942 + 1.5625 t = -2.840141942 + 1.5625 Combine like terms: -2.840141942 + 1.5625 = -1.277641942 t = -1.277641942 Simplifying t = -1.277641942Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.402641942, -1.277641942}Solution
t = {4.402641942, -1.277641942}
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