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Simplifying x2 + 3x + 50 = 2x2 + 2x + -12 Reorder the terms: 50 + 3x + x2 = 2x2 + 2x + -12 Reorder the terms: 50 + 3x + x2 = -12 + 2x + 2x2 Solving 50 + 3x + x2 = -12 + 2x + 2x2 Solving for variable 'x'. Reorder the terms: 50 + 12 + 3x + -2x + x2 + -2x2 = -12 + 2x + 2x2 + 12 + -2x + -2x2 Combine like terms: 50 + 12 = 62 62 + 3x + -2x + x2 + -2x2 = -12 + 2x + 2x2 + 12 + -2x + -2x2 Combine like terms: 3x + -2x = 1x 62 + 1x + x2 + -2x2 = -12 + 2x + 2x2 + 12 + -2x + -2x2 Combine like terms: x2 + -2x2 = -1x2 62 + 1x + -1x2 = -12 + 2x + 2x2 + 12 + -2x + -2x2 Reorder the terms: 62 + 1x + -1x2 = -12 + 12 + 2x + -2x + 2x2 + -2x2 Combine like terms: -12 + 12 = 0 62 + 1x + -1x2 = 0 + 2x + -2x + 2x2 + -2x2 62 + 1x + -1x2 = 2x + -2x + 2x2 + -2x2 Combine like terms: 2x + -2x = 0 62 + 1x + -1x2 = 0 + 2x2 + -2x2 62 + 1x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 62 + 1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -62 + -1x + x2 = 0 Move the constant term to the right: Add '62' to each side of the equation. -62 + -1x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + -1x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + -1x + x2 = 0 + 62 -1x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 -1x + x2 = 62 The x term is -1x. 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. -1x + 0.25 + x2 = 62 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 62 + 0.25 Combine like terms: 62 + 0.25 = 62.25 0.25 + -1x + x2 = 62.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (x + -0.5) equal to 7.889866919 and -7.889866919.Subproblem 1
x + -0.5 = 7.889866919 Simplifying x + -0.5 = 7.889866919 Reorder the terms: -0.5 + x = 7.889866919 Solving -0.5 + x = 7.889866919 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 = 7.889866919 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 7.889866919 + 0.5 x = 7.889866919 + 0.5 Combine like terms: 7.889866919 + 0.5 = 8.389866919 x = 8.389866919 Simplifying x = 8.389866919Subproblem 2
x + -0.5 = -7.889866919 Simplifying x + -0.5 = -7.889866919 Reorder the terms: -0.5 + x = -7.889866919 Solving -0.5 + x = -7.889866919 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 = -7.889866919 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -7.889866919 + 0.5 x = -7.889866919 + 0.5 Combine like terms: -7.889866919 + 0.5 = -7.389866919 x = -7.389866919 Simplifying x = -7.389866919Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.389866919, -7.389866919}
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