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Simplifying 8x2 + 2x + -13 = 0 Reorder the terms: -13 + 2x + 8x2 = 0 Solving -13 + 2x + 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'. -1.625 + 0.25x + x2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + 0.25x + 1.625 + x2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + 0.25x + x2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + 0.25x + x2 = 0 + 1.625 0.25x + x2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 0.25x + x2 = 1.625 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 1.625 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 1.625 + 0.015625 Combine like terms: 1.625 + 0.015625 = 1.640625 0.015625 + 0.25x + x2 = 1.640625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (x + 0.125) equal to 1.280868846 and -1.280868846.Subproblem 1
x + 0.125 = 1.280868846 Simplifying x + 0.125 = 1.280868846 Reorder the terms: 0.125 + x = 1.280868846 Solving 0.125 + x = 1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 1.280868846 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 1.280868846 + -0.125 x = 1.280868846 + -0.125 Combine like terms: 1.280868846 + -0.125 = 1.155868846 x = 1.155868846 Simplifying x = 1.155868846Subproblem 2
x + 0.125 = -1.280868846 Simplifying x + 0.125 = -1.280868846 Reorder the terms: 0.125 + x = -1.280868846 Solving 0.125 + x = -1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -1.280868846 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -1.280868846 + -0.125 x = -1.280868846 + -0.125 Combine like terms: -1.280868846 + -0.125 = -1.405868846 x = -1.405868846 Simplifying x = -1.405868846Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.155868846, -1.405868846}
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