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Simplifying 4x(2x + -9) + -2(5x + -6) = 0 Reorder the terms: 4x(-9 + 2x) + -2(5x + -6) = 0 (-9 * 4x + 2x * 4x) + -2(5x + -6) = 0 (-36x + 8x2) + -2(5x + -6) = 0 Reorder the terms: -36x + 8x2 + -2(-6 + 5x) = 0 -36x + 8x2 + (-6 * -2 + 5x * -2) = 0 -36x + 8x2 + (12 + -10x) = 0 Reorder the terms: 12 + -36x + -10x + 8x2 = 0 Combine like terms: -36x + -10x = -46x 12 + -46x + 8x2 = 0 Solving 12 + -46x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -23x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -23x + 4x2)' equal to zero and attempt to solve: Simplifying 6 + -23x + 4x2 = 0 Solving 6 + -23x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.5 + -5.75x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -5.75x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -5.75x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -5.75x + x2 = 0 + -1.5 -5.75x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -5.75x + x2 = -1.5 The x term is -5.75x. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75x + 8.265625 + x2 = -1.5 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = -1.5 + 8.265625 Combine like terms: -1.5 + 8.265625 = 6.765625 8.265625 + -5.75x + x2 = 6.765625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 6.765625 Calculate the square root of the right side: 2.601081506 Break this problem into two subproblems by setting (x + -2.875) equal to 2.601081506 and -2.601081506.Subproblem 1
x + -2.875 = 2.601081506 Simplifying x + -2.875 = 2.601081506 Reorder the terms: -2.875 + x = 2.601081506 Solving -2.875 + x = 2.601081506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = 2.601081506 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 2.601081506 + 2.875 x = 2.601081506 + 2.875 Combine like terms: 2.601081506 + 2.875 = 5.476081506 x = 5.476081506 Simplifying x = 5.476081506Subproblem 2
x + -2.875 = -2.601081506 Simplifying x + -2.875 = -2.601081506 Reorder the terms: -2.875 + x = -2.601081506 Solving -2.875 + x = -2.601081506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = -2.601081506 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -2.601081506 + 2.875 x = -2.601081506 + 2.875 Combine like terms: -2.601081506 + 2.875 = 0.273918494 x = 0.273918494 Simplifying x = 0.273918494Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.476081506, 0.273918494}Solution
x = {5.476081506, 0.273918494}
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