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Simplifying t2 + -23t + -625 = 0 Reorder the terms: -625 + -23t + t2 = 0 Solving -625 + -23t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '625' to each side of the equation. -625 + -23t + 625 + t2 = 0 + 625 Reorder the terms: -625 + 625 + -23t + t2 = 0 + 625 Combine like terms: -625 + 625 = 0 0 + -23t + t2 = 0 + 625 -23t + t2 = 0 + 625 Combine like terms: 0 + 625 = 625 -23t + t2 = 625 The t term is -23t. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23t + 132.25 + t2 = 625 + 132.25 Reorder the terms: 132.25 + -23t + t2 = 625 + 132.25 Combine like terms: 625 + 132.25 = 757.25 132.25 + -23t + t2 = 757.25 Factor a perfect square on the left side: (t + -11.5)(t + -11.5) = 757.25 Calculate the square root of the right side: 27.518175812 Break this problem into two subproblems by setting (t + -11.5) equal to 27.518175812 and -27.518175812.Subproblem 1
t + -11.5 = 27.518175812 Simplifying t + -11.5 = 27.518175812 Reorder the terms: -11.5 + t = 27.518175812 Solving -11.5 + t = 27.518175812 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + t = 27.518175812 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + t = 27.518175812 + 11.5 t = 27.518175812 + 11.5 Combine like terms: 27.518175812 + 11.5 = 39.018175812 t = 39.018175812 Simplifying t = 39.018175812Subproblem 2
t + -11.5 = -27.518175812 Simplifying t + -11.5 = -27.518175812 Reorder the terms: -11.5 + t = -27.518175812 Solving -11.5 + t = -27.518175812 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + t = -27.518175812 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + t = -27.518175812 + 11.5 t = -27.518175812 + 11.5 Combine like terms: -27.518175812 + 11.5 = -16.018175812 t = -16.018175812 Simplifying t = -16.018175812Solution
The solution to the problem is based on the solutions from the subproblems. t = {39.018175812, -16.018175812}
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