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Simplifying x2 + -13x + 36 = 2x2 + -16 + 32 Reorder the terms: 36 + -13x + x2 = 2x2 + -16 + 32 Reorder the terms: 36 + -13x + x2 = -16 + 32 + 2x2 Combine like terms: -16 + 32 = 16 36 + -13x + x2 = 16 + 2x2 Solving 36 + -13x + x2 = 16 + 2x2 Solving for variable 'x'. Reorder the terms: 36 + -16 + -13x + x2 + -2x2 = 16 + 2x2 + -16 + -2x2 Combine like terms: 36 + -16 = 20 20 + -13x + x2 + -2x2 = 16 + 2x2 + -16 + -2x2 Combine like terms: x2 + -2x2 = -1x2 20 + -13x + -1x2 = 16 + 2x2 + -16 + -2x2 Reorder the terms: 20 + -13x + -1x2 = 16 + -16 + 2x2 + -2x2 Combine like terms: 16 + -16 = 0 20 + -13x + -1x2 = 0 + 2x2 + -2x2 20 + -13x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 20 + -13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + 13x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 13x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 13x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 13x + x2 = 0 + 20 13x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 13x + x2 = 20 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 20 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 20 + 42.25 Combine like terms: 20 + 42.25 = 62.25 42.25 + 13x + x2 = 62.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (x + 6.5) equal to 7.889866919 and -7.889866919.Subproblem 1
x + 6.5 = 7.889866919 Simplifying x + 6.5 = 7.889866919 Reorder the terms: 6.5 + x = 7.889866919 Solving 6.5 + x = 7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 7.889866919 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 7.889866919 + -6.5 x = 7.889866919 + -6.5 Combine like terms: 7.889866919 + -6.5 = 1.389866919 x = 1.389866919 Simplifying x = 1.389866919Subproblem 2
x + 6.5 = -7.889866919 Simplifying x + 6.5 = -7.889866919 Reorder the terms: 6.5 + x = -7.889866919 Solving 6.5 + x = -7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -7.889866919 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -7.889866919 + -6.5 x = -7.889866919 + -6.5 Combine like terms: -7.889866919 + -6.5 = -14.389866919 x = -14.389866919 Simplifying x = -14.389866919Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.389866919, -14.389866919}
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