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Simplifying x2 + -22.5x + -112.5 = 0 Reorder the terms: -112.5 + -22.5x + x2 = 0 Solving -112.5 + -22.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '112.5' to each side of the equation. -112.5 + -22.5x + 112.5 + x2 = 0 + 112.5 Reorder the terms: -112.5 + 112.5 + -22.5x + x2 = 0 + 112.5 Combine like terms: -112.5 + 112.5 = 0.0 0.0 + -22.5x + x2 = 0 + 112.5 -22.5x + x2 = 0 + 112.5 Combine like terms: 0 + 112.5 = 112.5 -22.5x + x2 = 112.5 The x term is -22.5x. Take half its coefficient (-11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. -22.5x + 126.5625 + x2 = 112.5 + 126.5625 Reorder the terms: 126.5625 + -22.5x + x2 = 112.5 + 126.5625 Combine like terms: 112.5 + 126.5625 = 239.0625 126.5625 + -22.5x + x2 = 239.0625 Factor a perfect square on the left side: (x + -11.25)(x + -11.25) = 239.0625 Calculate the square root of the right side: 15.461646096 Break this problem into two subproblems by setting (x + -11.25) equal to 15.461646096 and -15.461646096.Subproblem 1
x + -11.25 = 15.461646096 Simplifying x + -11.25 = 15.461646096 Reorder the terms: -11.25 + x = 15.461646096 Solving -11.25 + x = 15.461646096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = 15.461646096 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = 15.461646096 + 11.25 x = 15.461646096 + 11.25 Combine like terms: 15.461646096 + 11.25 = 26.711646096 x = 26.711646096 Simplifying x = 26.711646096Subproblem 2
x + -11.25 = -15.461646096 Simplifying x + -11.25 = -15.461646096 Reorder the terms: -11.25 + x = -15.461646096 Solving -11.25 + x = -15.461646096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = -15.461646096 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = -15.461646096 + 11.25 x = -15.461646096 + 11.25 Combine like terms: -15.461646096 + 11.25 = -4.211646096 x = -4.211646096 Simplifying x = -4.211646096Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.711646096, -4.211646096}
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