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Simplifying 12x + -6 + (5 + -1x) * x = 4 Reorder the terms for easier multiplication: 12x + -6 + x(5 + -1x) = 4 12x + -6 + (5 * x + -1x * x) = 4 12x + -6 + (5x + -1x2) = 4 Reorder the terms: -6 + 12x + 5x + -1x2 = 4 Combine like terms: 12x + 5x = 17x -6 + 17x + -1x2 = 4 Solving -6 + 17x + -1x2 = 4 Solving for variable 'x'. Reorder the terms: -6 + -4 + 17x + -1x2 = 4 + -4 Combine like terms: -6 + -4 = -10 -10 + 17x + -1x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -10 + 17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 10 + -17x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -17x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -17x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -17x + x2 = 0 + -10 -17x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -17x + x2 = -10 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -10 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -10 + 72.25 Combine like terms: -10 + 72.25 = 62.25 72.25 + -17x + x2 = 62.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (x + -8.5) equal to 7.889866919 and -7.889866919.Subproblem 1
x + -8.5 = 7.889866919 Simplifying x + -8.5 = 7.889866919 Reorder the terms: -8.5 + x = 7.889866919 Solving -8.5 + x = 7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 7.889866919 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 7.889866919 + 8.5 x = 7.889866919 + 8.5 Combine like terms: 7.889866919 + 8.5 = 16.389866919 x = 16.389866919 Simplifying x = 16.389866919Subproblem 2
x + -8.5 = -7.889866919 Simplifying x + -8.5 = -7.889866919 Reorder the terms: -8.5 + x = -7.889866919 Solving -8.5 + x = -7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -7.889866919 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -7.889866919 + 8.5 x = -7.889866919 + 8.5 Combine like terms: -7.889866919 + 8.5 = 0.610133081 x = 0.610133081 Simplifying x = 0.610133081Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.389866919, 0.610133081}
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