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Simplifying 8x2 + -29x + -15 = 0 Reorder the terms: -15 + -29x + 8x2 = 0 Solving -15 + -29x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.875 + -3.625x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -3.625x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -3.625x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -3.625x + x2 = 0 + 1.875 -3.625x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -3.625x + x2 = 1.875 The x term is -3.625x. Take half its coefficient (-1.8125). Square it (3.28515625) and add it to both sides. Add '3.28515625' to each side of the equation. -3.625x + 3.28515625 + x2 = 1.875 + 3.28515625 Reorder the terms: 3.28515625 + -3.625x + x2 = 1.875 + 3.28515625 Combine like terms: 1.875 + 3.28515625 = 5.16015625 3.28515625 + -3.625x + x2 = 5.16015625 Factor a perfect square on the left side: (x + -1.8125)(x + -1.8125) = 5.16015625 Calculate the square root of the right side: 2.271597731 Break this problem into two subproblems by setting (x + -1.8125) equal to 2.271597731 and -2.271597731.Subproblem 1
x + -1.8125 = 2.271597731 Simplifying x + -1.8125 = 2.271597731 Reorder the terms: -1.8125 + x = 2.271597731 Solving -1.8125 + x = 2.271597731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8125' to each side of the equation. -1.8125 + 1.8125 + x = 2.271597731 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + x = 2.271597731 + 1.8125 x = 2.271597731 + 1.8125 Combine like terms: 2.271597731 + 1.8125 = 4.084097731 x = 4.084097731 Simplifying x = 4.084097731Subproblem 2
x + -1.8125 = -2.271597731 Simplifying x + -1.8125 = -2.271597731 Reorder the terms: -1.8125 + x = -2.271597731 Solving -1.8125 + x = -2.271597731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8125' to each side of the equation. -1.8125 + 1.8125 + x = -2.271597731 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + x = -2.271597731 + 1.8125 x = -2.271597731 + 1.8125 Combine like terms: -2.271597731 + 1.8125 = -0.459097731 x = -0.459097731 Simplifying x = -0.459097731Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.084097731, -0.459097731}
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