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Simplifying 8t2 + -23t + 10 = 0 Reorder the terms: 10 + -23t + 8t2 = 0 Solving 10 + -23t + 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'. 1.25 + -2.875t + t2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -2.875t + -1.25 + t2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -2.875t + t2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -2.875t + t2 = 0 + -1.25 -2.875t + t2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -2.875t + t2 = -1.25 The t term is -2.875t. Take half its coefficient (-1.4375). Square it (2.06640625) and add it to both sides. Add '2.06640625' to each side of the equation. -2.875t + 2.06640625 + t2 = -1.25 + 2.06640625 Reorder the terms: 2.06640625 + -2.875t + t2 = -1.25 + 2.06640625 Combine like terms: -1.25 + 2.06640625 = 0.81640625 2.06640625 + -2.875t + t2 = 0.81640625 Factor a perfect square on the left side: (t + -1.4375)(t + -1.4375) = 0.81640625 Calculate the square root of the right side: 0.903552018 Break this problem into two subproblems by setting (t + -1.4375) equal to 0.903552018 and -0.903552018.Subproblem 1
t + -1.4375 = 0.903552018 Simplifying t + -1.4375 = 0.903552018 Reorder the terms: -1.4375 + t = 0.903552018 Solving -1.4375 + t = 0.903552018 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + t = 0.903552018 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + t = 0.903552018 + 1.4375 t = 0.903552018 + 1.4375 Combine like terms: 0.903552018 + 1.4375 = 2.341052018 t = 2.341052018 Simplifying t = 2.341052018Subproblem 2
t + -1.4375 = -0.903552018 Simplifying t + -1.4375 = -0.903552018 Reorder the terms: -1.4375 + t = -0.903552018 Solving -1.4375 + t = -0.903552018 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + t = -0.903552018 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + t = -0.903552018 + 1.4375 t = -0.903552018 + 1.4375 Combine like terms: -0.903552018 + 1.4375 = 0.533947982 t = 0.533947982 Simplifying t = 0.533947982Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.341052018, 0.533947982}
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