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Simplifying x(x + -22) = 112 Reorder the terms: x(-22 + x) = 112 (-22 * x + x * x) = 112 (-22x + x2) = 112 Solving -22x + x2 = 112 Solving for variable 'x'. Reorder the terms: -112 + -22x + x2 = 112 + -112 Combine like terms: 112 + -112 = 0 -112 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '112' to each side of the equation. -112 + -22x + 112 + x2 = 0 + 112 Reorder the terms: -112 + 112 + -22x + x2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + -22x + x2 = 0 + 112 -22x + x2 = 0 + 112 Combine like terms: 0 + 112 = 112 -22x + x2 = 112 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = 112 + 121 Reorder the terms: 121 + -22x + x2 = 112 + 121 Combine like terms: 112 + 121 = 233 121 + -22x + x2 = 233 Factor a perfect square on the left side: (x + -11)(x + -11) = 233 Calculate the square root of the right side: 15.264337522 Break this problem into two subproblems by setting (x + -11) equal to 15.264337522 and -15.264337522.Subproblem 1
x + -11 = 15.264337522 Simplifying x + -11 = 15.264337522 Reorder the terms: -11 + x = 15.264337522 Solving -11 + x = 15.264337522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 15.264337522 + 11 Combine like terms: -11 + 11 = 0 0 + x = 15.264337522 + 11 x = 15.264337522 + 11 Combine like terms: 15.264337522 + 11 = 26.264337522 x = 26.264337522 Simplifying x = 26.264337522Subproblem 2
x + -11 = -15.264337522 Simplifying x + -11 = -15.264337522 Reorder the terms: -11 + x = -15.264337522 Solving -11 + x = -15.264337522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -15.264337522 + 11 Combine like terms: -11 + 11 = 0 0 + x = -15.264337522 + 11 x = -15.264337522 + 11 Combine like terms: -15.264337522 + 11 = -4.264337522 x = -4.264337522 Simplifying x = -4.264337522Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.264337522, -4.264337522}
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