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Simplifying x2 + 12 + -9x + 135 = 622 Reorder the terms: 12 + 135 + -9x + x2 = 622 Combine like terms: 12 + 135 = 147 147 + -9x + x2 = 622 Solving 147 + -9x + x2 = 622 Solving for variable 'x'. Reorder the terms: 147 + -622 + -9x + x2 = 622 + -622 Combine like terms: 147 + -622 = -475 -475 + -9x + x2 = 622 + -622 Combine like terms: 622 + -622 = 0 -475 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '475' to each side of the equation. -475 + -9x + 475 + x2 = 0 + 475 Reorder the terms: -475 + 475 + -9x + x2 = 0 + 475 Combine like terms: -475 + 475 = 0 0 + -9x + x2 = 0 + 475 -9x + x2 = 0 + 475 Combine like terms: 0 + 475 = 475 -9x + x2 = 475 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 = 475 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 475 + 20.25 Combine like terms: 475 + 20.25 = 495.25 20.25 + -9x + x2 = 495.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 495.25 Calculate the square root of the right side: 22.254213084 Break this problem into two subproblems by setting (x + -4.5) equal to 22.254213084 and -22.254213084.Subproblem 1
x + -4.5 = 22.254213084 Simplifying x + -4.5 = 22.254213084 Reorder the terms: -4.5 + x = 22.254213084 Solving -4.5 + x = 22.254213084 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 = 22.254213084 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 22.254213084 + 4.5 x = 22.254213084 + 4.5 Combine like terms: 22.254213084 + 4.5 = 26.754213084 x = 26.754213084 Simplifying x = 26.754213084Subproblem 2
x + -4.5 = -22.254213084 Simplifying x + -4.5 = -22.254213084 Reorder the terms: -4.5 + x = -22.254213084 Solving -4.5 + x = -22.254213084 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 = -22.254213084 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -22.254213084 + 4.5 x = -22.254213084 + 4.5 Combine like terms: -22.254213084 + 4.5 = -17.754213084 x = -17.754213084 Simplifying x = -17.754213084Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.754213084, -17.754213084}
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