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Simplifying (x + 6)(x + -9) + -6 = 0 Reorder the terms: (6 + x)(x + -9) + -6 = 0 Reorder the terms: (6 + x)(-9 + x) + -6 = 0 Multiply (6 + x) * (-9 + x) (6(-9 + x) + x(-9 + x)) + -6 = 0 ((-9 * 6 + x * 6) + x(-9 + x)) + -6 = 0 ((-54 + 6x) + x(-9 + x)) + -6 = 0 (-54 + 6x + (-9 * x + x * x)) + -6 = 0 (-54 + 6x + (-9x + x2)) + -6 = 0 Combine like terms: 6x + -9x = -3x (-54 + -3x + x2) + -6 = 0 Reorder the terms: -54 + -6 + -3x + x2 = 0 Combine like terms: -54 + -6 = -60 -60 + -3x + x2 = 0 Solving -60 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -3x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -3x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -3x + x2 = 0 + 60 -3x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -3x + x2 = 60 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 60 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 60 + 2.25 Combine like terms: 60 + 2.25 = 62.25 2.25 + -3x + x2 = 62.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (x + -1.5) equal to 7.889866919 and -7.889866919.Subproblem 1
x + -1.5 = 7.889866919 Simplifying x + -1.5 = 7.889866919 Reorder the terms: -1.5 + x = 7.889866919 Solving -1.5 + x = 7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 7.889866919 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 7.889866919 + 1.5 x = 7.889866919 + 1.5 Combine like terms: 7.889866919 + 1.5 = 9.389866919 x = 9.389866919 Simplifying x = 9.389866919Subproblem 2
x + -1.5 = -7.889866919 Simplifying x + -1.5 = -7.889866919 Reorder the terms: -1.5 + x = -7.889866919 Solving -1.5 + x = -7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -7.889866919 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -7.889866919 + 1.5 x = -7.889866919 + 1.5 Combine like terms: -7.889866919 + 1.5 = -6.389866919 x = -6.389866919 Simplifying x = -6.389866919Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.389866919, -6.389866919}
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