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Simplifying x2 + -5x + -33 = 4x + 9 Reorder the terms: -33 + -5x + x2 = 4x + 9 Reorder the terms: -33 + -5x + x2 = 9 + 4x Solving -33 + -5x + x2 = 9 + 4x Solving for variable 'x'. Reorder the terms: -33 + -9 + -5x + -4x + x2 = 9 + 4x + -9 + -4x Combine like terms: -33 + -9 = -42 -42 + -5x + -4x + x2 = 9 + 4x + -9 + -4x Combine like terms: -5x + -4x = -9x -42 + -9x + x2 = 9 + 4x + -9 + -4x Reorder the terms: -42 + -9x + x2 = 9 + -9 + 4x + -4x Combine like terms: 9 + -9 = 0 -42 + -9x + x2 = 0 + 4x + -4x -42 + -9x + x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -42 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -9x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + -9x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -9x + x2 = 0 + 42 -9x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 -9x + x2 = 42 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 42 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 42 + 20.25 Combine like terms: 42 + 20.25 = 62.25 20.25 + -9x + x2 = 62.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (x + -4.5) equal to 7.889866919 and -7.889866919.Subproblem 1
x + -4.5 = 7.889866919 Simplifying x + -4.5 = 7.889866919 Reorder the terms: -4.5 + x = 7.889866919 Solving -4.5 + x = 7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 7.889866919 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 7.889866919 + 4.5 x = 7.889866919 + 4.5 Combine like terms: 7.889866919 + 4.5 = 12.389866919 x = 12.389866919 Simplifying x = 12.389866919Subproblem 2
x + -4.5 = -7.889866919 Simplifying x + -4.5 = -7.889866919 Reorder the terms: -4.5 + x = -7.889866919 Solving -4.5 + x = -7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -7.889866919 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -7.889866919 + 4.5 x = -7.889866919 + 4.5 Combine like terms: -7.889866919 + 4.5 = -3.389866919 x = -3.389866919 Simplifying x = -3.389866919Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.389866919, -3.389866919}
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