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Simplifying -2(x + -6) = 3x + -8x(x + -3) Reorder the terms: -2(-6 + x) = 3x + -8x(x + -3) (-6 * -2 + x * -2) = 3x + -8x(x + -3) (12 + -2x) = 3x + -8x(x + -3) Reorder the terms: 12 + -2x = 3x + -8x(-3 + x) 12 + -2x = 3x + (-3 * -8x + x * -8x) 12 + -2x = 3x + (24x + -8x2) Combine like terms: 3x + 24x = 27x 12 + -2x = 27x + -8x2 Solving 12 + -2x = 27x + -8x2 Solving for variable 'x'. Combine like terms: -2x + -27x = -29x 12 + -29x + 8x2 = 27x + -8x2 + -27x + 8x2 Reorder the terms: 12 + -29x + 8x2 = 27x + -27x + -8x2 + 8x2 Combine like terms: 27x + -27x = 0 12 + -29x + 8x2 = 0 + -8x2 + 8x2 12 + -29x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 12 + -29x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.5 + -3.625x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -3.625x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -3.625x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -3.625x + x2 = 0 + -1.5 -3.625x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -3.625x + x2 = -1.5 The x term is -3.625x. Take half its coefficient (-1.8125). Square it (3.28515625) and add it to both sides. Add '3.28515625' to each side of the equation. -3.625x + 3.28515625 + x2 = -1.5 + 3.28515625 Reorder the terms: 3.28515625 + -3.625x + x2 = -1.5 + 3.28515625 Combine like terms: -1.5 + 3.28515625 = 1.78515625 3.28515625 + -3.625x + x2 = 1.78515625 Factor a perfect square on the left side: (x + -1.8125)(x + -1.8125) = 1.78515625 Calculate the square root of the right side: 1.336097395 Break this problem into two subproblems by setting (x + -1.8125) equal to 1.336097395 and -1.336097395.Subproblem 1
x + -1.8125 = 1.336097395 Simplifying x + -1.8125 = 1.336097395 Reorder the terms: -1.8125 + x = 1.336097395 Solving -1.8125 + x = 1.336097395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8125' to each side of the equation. -1.8125 + 1.8125 + x = 1.336097395 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + x = 1.336097395 + 1.8125 x = 1.336097395 + 1.8125 Combine like terms: 1.336097395 + 1.8125 = 3.148597395 x = 3.148597395 Simplifying x = 3.148597395Subproblem 2
x + -1.8125 = -1.336097395 Simplifying x + -1.8125 = -1.336097395 Reorder the terms: -1.8125 + x = -1.336097395 Solving -1.8125 + x = -1.336097395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8125' to each side of the equation. -1.8125 + 1.8125 + x = -1.336097395 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + x = -1.336097395 + 1.8125 x = -1.336097395 + 1.8125 Combine like terms: -1.336097395 + 1.8125 = 0.476402605 x = 0.476402605 Simplifying x = 0.476402605Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.148597395, 0.476402605}
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