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Simplifying x2 + -8x = 2(4x + 12) Reorder the terms: -8x + x2 = 2(4x + 12) Reorder the terms: -8x + x2 = 2(12 + 4x) -8x + x2 = (12 * 2 + 4x * 2) -8x + x2 = (24 + 8x) Solving -8x + x2 = 24 + 8x Solving for variable 'x'. Reorder the terms: -24 + -8x + -8x + x2 = 24 + 8x + -24 + -8x Combine like terms: -8x + -8x = -16x -24 + -16x + x2 = 24 + 8x + -24 + -8x Reorder the terms: -24 + -16x + x2 = 24 + -24 + 8x + -8x Combine like terms: 24 + -24 = 0 -24 + -16x + x2 = 0 + 8x + -8x -24 + -16x + x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -24 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -16x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -16x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -16x + x2 = 0 + 24 -16x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -16x + x2 = 24 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 24 + 64 Reorder the terms: 64 + -16x + x2 = 24 + 64 Combine like terms: 24 + 64 = 88 64 + -16x + x2 = 88 Factor a perfect square on the left side: (x + -8)(x + -8) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (x + -8) equal to 9.38083152 and -9.38083152.Subproblem 1
x + -8 = 9.38083152 Simplifying x + -8 = 9.38083152 Reorder the terms: -8 + x = 9.38083152 Solving -8 + x = 9.38083152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 9.38083152 + 8 Combine like terms: -8 + 8 = 0 0 + x = 9.38083152 + 8 x = 9.38083152 + 8 Combine like terms: 9.38083152 + 8 = 17.38083152 x = 17.38083152 Simplifying x = 17.38083152Subproblem 2
x + -8 = -9.38083152 Simplifying x + -8 = -9.38083152 Reorder the terms: -8 + x = -9.38083152 Solving -8 + x = -9.38083152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -9.38083152 + 8 Combine like terms: -8 + 8 = 0 0 + x = -9.38083152 + 8 x = -9.38083152 + 8 Combine like terms: -9.38083152 + 8 = -1.38083152 x = -1.38083152 Simplifying x = -1.38083152Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.38083152, -1.38083152}
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