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Simplifying 8x2 + -2x + -45 * 4x + 9 = 0 Multiply -45 * 4 8x2 + -2x + -180x + 9 = 0 Reorder the terms: 9 + -2x + -180x + 8x2 = 0 Combine like terms: -2x + -180x = -182x 9 + -182x + 8x2 = 0 Solving 9 + -182x + 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'. 1.125 + -22.75x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -22.75x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -22.75x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -22.75x + x2 = 0 + -1.125 -22.75x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -22.75x + x2 = -1.125 The x term is -22.75x. Take half its coefficient (-11.375). Square it (129.390625) and add it to both sides. Add '129.390625' to each side of the equation. -22.75x + 129.390625 + x2 = -1.125 + 129.390625 Reorder the terms: 129.390625 + -22.75x + x2 = -1.125 + 129.390625 Combine like terms: -1.125 + 129.390625 = 128.265625 129.390625 + -22.75x + x2 = 128.265625 Factor a perfect square on the left side: (x + -11.375)(x + -11.375) = 128.265625 Calculate the square root of the right side: 11.325441492 Break this problem into two subproblems by setting (x + -11.375) equal to 11.325441492 and -11.325441492.Subproblem 1
x + -11.375 = 11.325441492 Simplifying x + -11.375 = 11.325441492 Reorder the terms: -11.375 + x = 11.325441492 Solving -11.375 + x = 11.325441492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.375' to each side of the equation. -11.375 + 11.375 + x = 11.325441492 + 11.375 Combine like terms: -11.375 + 11.375 = 0.000 0.000 + x = 11.325441492 + 11.375 x = 11.325441492 + 11.375 Combine like terms: 11.325441492 + 11.375 = 22.700441492 x = 22.700441492 Simplifying x = 22.700441492Subproblem 2
x + -11.375 = -11.325441492 Simplifying x + -11.375 = -11.325441492 Reorder the terms: -11.375 + x = -11.325441492 Solving -11.375 + x = -11.325441492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.375' to each side of the equation. -11.375 + 11.375 + x = -11.325441492 + 11.375 Combine like terms: -11.375 + 11.375 = 0.000 0.000 + x = -11.325441492 + 11.375 x = -11.325441492 + 11.375 Combine like terms: -11.325441492 + 11.375 = 0.049558508 x = 0.049558508 Simplifying x = 0.049558508Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.700441492, 0.049558508}
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