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Simplifying -8t2 + 14t + 5 = 0 Reorder the terms: 5 + 14t + -8t2 = 0 Solving 5 + 14t + -8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.625 + -1.75t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -1.75t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -1.75t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -1.75t + t2 = 0 + 0.625 -1.75t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -1.75t + t2 = 0.625 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 = 0.625 + 0.765625 Reorder the terms: 0.765625 + -1.75t + t2 = 0.625 + 0.765625 Combine like terms: 0.625 + 0.765625 = 1.390625 0.765625 + -1.75t + t2 = 1.390625 Factor a perfect square on the left side: (t + -0.875)(t + -0.875) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (t + -0.875) equal to 1.179247642 and -1.179247642.Subproblem 1
t + -0.875 = 1.179247642 Simplifying t + -0.875 = 1.179247642 Reorder the terms: -0.875 + t = 1.179247642 Solving -0.875 + t = 1.179247642 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 = 1.179247642 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + t = 1.179247642 + 0.875 t = 1.179247642 + 0.875 Combine like terms: 1.179247642 + 0.875 = 2.054247642 t = 2.054247642 Simplifying t = 2.054247642Subproblem 2
t + -0.875 = -1.179247642 Simplifying t + -0.875 = -1.179247642 Reorder the terms: -0.875 + t = -1.179247642 Solving -0.875 + t = -1.179247642 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 = -1.179247642 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + t = -1.179247642 + 0.875 t = -1.179247642 + 0.875 Combine like terms: -1.179247642 + 0.875 = -0.304247642 t = -0.304247642 Simplifying t = -0.304247642Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.054247642, -0.304247642}
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