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Simplifying 4t2 + -45t + -99 = 0 Reorder the terms: -99 + -45t + 4t2 = 0 Solving -99 + -45t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -24.75 + -11.25t + t2 = 0 Move the constant term to the right: Add '24.75' to each side of the equation. -24.75 + -11.25t + 24.75 + t2 = 0 + 24.75 Reorder the terms: -24.75 + 24.75 + -11.25t + t2 = 0 + 24.75 Combine like terms: -24.75 + 24.75 = 0.00 0.00 + -11.25t + t2 = 0 + 24.75 -11.25t + t2 = 0 + 24.75 Combine like terms: 0 + 24.75 = 24.75 -11.25t + t2 = 24.75 The t term is -11.25t. Take half its coefficient (-5.625). Square it (31.640625) and add it to both sides. Add '31.640625' to each side of the equation. -11.25t + 31.640625 + t2 = 24.75 + 31.640625 Reorder the terms: 31.640625 + -11.25t + t2 = 24.75 + 31.640625 Combine like terms: 24.75 + 31.640625 = 56.390625 31.640625 + -11.25t + t2 = 56.390625 Factor a perfect square on the left side: (t + -5.625)(t + -5.625) = 56.390625 Calculate the square root of the right side: 7.509369148 Break this problem into two subproblems by setting (t + -5.625) equal to 7.509369148 and -7.509369148.Subproblem 1
t + -5.625 = 7.509369148 Simplifying t + -5.625 = 7.509369148 Reorder the terms: -5.625 + t = 7.509369148 Solving -5.625 + t = 7.509369148 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + t = 7.509369148 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + t = 7.509369148 + 5.625 t = 7.509369148 + 5.625 Combine like terms: 7.509369148 + 5.625 = 13.134369148 t = 13.134369148 Simplifying t = 13.134369148Subproblem 2
t + -5.625 = -7.509369148 Simplifying t + -5.625 = -7.509369148 Reorder the terms: -5.625 + t = -7.509369148 Solving -5.625 + t = -7.509369148 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + t = -7.509369148 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + t = -7.509369148 + 5.625 t = -7.509369148 + 5.625 Combine like terms: -7.509369148 + 5.625 = -1.884369148 t = -1.884369148 Simplifying t = -1.884369148Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.134369148, -1.884369148}
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