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Simplifying x2 + 0.713x + -0.13 = 0 Reorder the terms: -0.13 + 0.713x + x2 = 0 Solving -0.13 + 0.713x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.13' to each side of the equation. -0.13 + 0.713x + 0.13 + x2 = 0 + 0.13 Reorder the terms: -0.13 + 0.13 + 0.713x + x2 = 0 + 0.13 Combine like terms: -0.13 + 0.13 = 0.00 0.00 + 0.713x + x2 = 0 + 0.13 0.713x + x2 = 0 + 0.13 Combine like terms: 0 + 0.13 = 0.13 0.713x + x2 = 0.13 The x term is 0.713x. Take half its coefficient (0.3565). Square it (0.12709225) and add it to both sides. Add '0.12709225' to each side of the equation. 0.713x + 0.12709225 + x2 = 0.13 + 0.12709225 Reorder the terms: 0.12709225 + 0.713x + x2 = 0.13 + 0.12709225 Combine like terms: 0.13 + 0.12709225 = 0.25709225 0.12709225 + 0.713x + x2 = 0.25709225 Factor a perfect square on the left side: (x + 0.3565)(x + 0.3565) = 0.25709225 Calculate the square root of the right side: 0.507042651 Break this problem into two subproblems by setting (x + 0.3565) equal to 0.507042651 and -0.507042651.Subproblem 1
x + 0.3565 = 0.507042651 Simplifying x + 0.3565 = 0.507042651 Reorder the terms: 0.3565 + x = 0.507042651 Solving 0.3565 + x = 0.507042651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3565' to each side of the equation. 0.3565 + -0.3565 + x = 0.507042651 + -0.3565 Combine like terms: 0.3565 + -0.3565 = 0.0000 0.0000 + x = 0.507042651 + -0.3565 x = 0.507042651 + -0.3565 Combine like terms: 0.507042651 + -0.3565 = 0.150542651 x = 0.150542651 Simplifying x = 0.150542651Subproblem 2
x + 0.3565 = -0.507042651 Simplifying x + 0.3565 = -0.507042651 Reorder the terms: 0.3565 + x = -0.507042651 Solving 0.3565 + x = -0.507042651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3565' to each side of the equation. 0.3565 + -0.3565 + x = -0.507042651 + -0.3565 Combine like terms: 0.3565 + -0.3565 = 0.0000 0.0000 + x = -0.507042651 + -0.3565 x = -0.507042651 + -0.3565 Combine like terms: -0.507042651 + -0.3565 = -0.863542651 x = -0.863542651 Simplifying x = -0.863542651Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.150542651, -0.863542651}
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