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Simplifying 0 = -1x2 + -11x + 32 Reorder the terms: 0 = 32 + -11x + -1x2 Solving 0 = 32 + -11x + -1x2 Solving for variable 'x'. Combine like terms: 0 + -32 = -32 -32 + 11x + x2 = 32 + -11x + -1x2 + -32 + 11x + x2 Reorder the terms: -32 + 11x + x2 = 32 + -32 + -11x + 11x + -1x2 + x2 Combine like terms: 32 + -32 = 0 -32 + 11x + x2 = 0 + -11x + 11x + -1x2 + x2 -32 + 11x + x2 = -11x + 11x + -1x2 + x2 Combine like terms: -11x + 11x = 0 -32 + 11x + x2 = 0 + -1x2 + x2 -32 + 11x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -32 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + 11x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 11x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 11x + x2 = 0 + 32 11x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 11x + x2 = 32 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 32 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 32 + 30.25 Combine like terms: 32 + 30.25 = 62.25 30.25 + 11x + x2 = 62.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (x + 5.5) equal to 7.889866919 and -7.889866919.Subproblem 1
x + 5.5 = 7.889866919 Simplifying x + 5.5 = 7.889866919 Reorder the terms: 5.5 + x = 7.889866919 Solving 5.5 + x = 7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 7.889866919 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 7.889866919 + -5.5 x = 7.889866919 + -5.5 Combine like terms: 7.889866919 + -5.5 = 2.389866919 x = 2.389866919 Simplifying x = 2.389866919Subproblem 2
x + 5.5 = -7.889866919 Simplifying x + 5.5 = -7.889866919 Reorder the terms: 5.5 + x = -7.889866919 Solving 5.5 + x = -7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -7.889866919 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -7.889866919 + -5.5 x = -7.889866919 + -5.5 Combine like terms: -7.889866919 + -5.5 = -13.389866919 x = -13.389866919 Simplifying x = -13.389866919Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.389866919, -13.389866919}
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