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Simplifying -16t2 + 12t + 900 = 0 Reorder the terms: 900 + 12t + -16t2 = 0 Solving 900 + 12t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(225 + 3t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(225 + 3t + -4t2)' equal to zero and attempt to solve: Simplifying 225 + 3t + -4t2 = 0 Solving 225 + 3t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -56.25 + -0.75t + t2 = 0 Move the constant term to the right: Add '56.25' to each side of the equation. -56.25 + -0.75t + 56.25 + t2 = 0 + 56.25 Reorder the terms: -56.25 + 56.25 + -0.75t + t2 = 0 + 56.25 Combine like terms: -56.25 + 56.25 = 0.00 0.00 + -0.75t + t2 = 0 + 56.25 -0.75t + t2 = 0 + 56.25 Combine like terms: 0 + 56.25 = 56.25 -0.75t + t2 = 56.25 The t term is -0.75t. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75t + 0.140625 + t2 = 56.25 + 0.140625 Reorder the terms: 0.140625 + -0.75t + t2 = 56.25 + 0.140625 Combine like terms: 56.25 + 0.140625 = 56.390625 0.140625 + -0.75t + t2 = 56.390625 Factor a perfect square on the left side: (t + -0.375)(t + -0.375) = 56.390625 Calculate the square root of the right side: 7.509369148 Break this problem into two subproblems by setting (t + -0.375) equal to 7.509369148 and -7.509369148.Subproblem 1
t + -0.375 = 7.509369148 Simplifying t + -0.375 = 7.509369148 Reorder the terms: -0.375 + t = 7.509369148 Solving -0.375 + t = 7.509369148 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + t = 7.509369148 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = 7.509369148 + 0.375 t = 7.509369148 + 0.375 Combine like terms: 7.509369148 + 0.375 = 7.884369148 t = 7.884369148 Simplifying t = 7.884369148Subproblem 2
t + -0.375 = -7.509369148 Simplifying t + -0.375 = -7.509369148 Reorder the terms: -0.375 + t = -7.509369148 Solving -0.375 + t = -7.509369148 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + t = -7.509369148 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = -7.509369148 + 0.375 t = -7.509369148 + 0.375 Combine like terms: -7.509369148 + 0.375 = -7.134369148 t = -7.134369148 Simplifying t = -7.134369148Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.884369148, -7.134369148}Solution
t = {7.884369148, -7.134369148}
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