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Simplifying 12 + -2x + -1x2 = 4 + -1x Solving 12 + -2x + -1x2 = 4 + -1x Solving for variable 'x'. Reorder the terms: 12 + -4 + -2x + x + -1x2 = 4 + -1x + -4 + x Combine like terms: 12 + -4 = 8 8 + -2x + x + -1x2 = 4 + -1x + -4 + x Combine like terms: -2x + x = -1x 8 + -1x + -1x2 = 4 + -1x + -4 + x Reorder the terms: 8 + -1x + -1x2 = 4 + -4 + -1x + x Combine like terms: 4 + -4 = 0 8 + -1x + -1x2 = 0 + -1x + x 8 + -1x + -1x2 = -1x + x Combine like terms: -1x + x = 0 8 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x + x2 = 0 + 8 x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 x + x2 = 8 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 8 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 8 + 0.25 Combine like terms: 8 + 0.25 = 8.25 1.25 + x2 = 8.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + 0.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x + 0.5 = 2.872281323 Simplifying x + 0.5 = 2.872281323 Reorder the terms: 0.5 + x = 2.872281323 Solving 0.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.872281323 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.872281323 + -0.5 x = 2.872281323 + -0.5 Combine like terms: 2.872281323 + -0.5 = 2.372281323 x = 2.372281323 Simplifying x = 2.372281323Subproblem 2
x + 0.5 = -2.872281323 Simplifying x + 0.5 = -2.872281323 Reorder the terms: 0.5 + x = -2.872281323 Solving 0.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.872281323 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.872281323 + -0.5 x = -2.872281323 + -0.5 Combine like terms: -2.872281323 + -0.5 = -3.372281323 x = -3.372281323 Simplifying x = -3.372281323Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.372281323, -3.372281323}
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