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Simplifying -16t2 + 28t = -250 Reorder the terms: 28t + -16t2 = -250 Solving 28t + -16t2 = -250 Solving for variable 't'. Reorder the terms: 250 + 28t + -16t2 = -250 + 250 Combine like terms: -250 + 250 = 0 250 + 28t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(125 + 14t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(125 + 14t + -8t2)' equal to zero and attempt to solve: Simplifying 125 + 14t + -8t2 = 0 Solving 125 + 14t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -15.625 + -1.75t + t2 = 0 Move the constant term to the right: Add '15.625' to each side of the equation. -15.625 + -1.75t + 15.625 + t2 = 0 + 15.625 Reorder the terms: -15.625 + 15.625 + -1.75t + t2 = 0 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + -1.75t + t2 = 0 + 15.625 -1.75t + t2 = 0 + 15.625 Combine like terms: 0 + 15.625 = 15.625 -1.75t + t2 = 15.625 The t term is -1.75t. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75t + 0.765625 + t2 = 15.625 + 0.765625 Reorder the terms: 0.765625 + -1.75t + t2 = 15.625 + 0.765625 Combine like terms: 15.625 + 0.765625 = 16.390625 0.765625 + -1.75t + t2 = 16.390625 Factor a perfect square on the left side: (t + -0.875)(t + -0.875) = 16.390625 Calculate the square root of the right side: 4.048533685 Break this problem into two subproblems by setting (t + -0.875) equal to 4.048533685 and -4.048533685.Subproblem 1
t + -0.875 = 4.048533685 Simplifying t + -0.875 = 4.048533685 Reorder the terms: -0.875 + t = 4.048533685 Solving -0.875 + t = 4.048533685 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + t = 4.048533685 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + t = 4.048533685 + 0.875 t = 4.048533685 + 0.875 Combine like terms: 4.048533685 + 0.875 = 4.923533685 t = 4.923533685 Simplifying t = 4.923533685Subproblem 2
t + -0.875 = -4.048533685 Simplifying t + -0.875 = -4.048533685 Reorder the terms: -0.875 + t = -4.048533685 Solving -0.875 + t = -4.048533685 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + t = -4.048533685 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + t = -4.048533685 + 0.875 t = -4.048533685 + 0.875 Combine like terms: -4.048533685 + 0.875 = -3.173533685 t = -3.173533685 Simplifying t = -3.173533685Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.923533685, -3.173533685}Solution
t = {4.923533685, -3.173533685}
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