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Simplifying x2 + -22x + 32 = 0 Reorder the terms: 32 + -22x + x2 = 0 Solving 32 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -22x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + -22x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -22x + x2 = 0 + -32 -22x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 -22x + x2 = -32 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 = -32 + 121 Reorder the terms: 121 + -22x + x2 = -32 + 121 Combine like terms: -32 + 121 = 89 121 + -22x + x2 = 89 Factor a perfect square on the left side: (x + -11)(x + -11) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (x + -11) equal to 9.433981132 and -9.433981132.Subproblem 1
x + -11 = 9.433981132 Simplifying x + -11 = 9.433981132 Reorder the terms: -11 + x = 9.433981132 Solving -11 + x = 9.433981132 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 = 9.433981132 + 11 Combine like terms: -11 + 11 = 0 0 + x = 9.433981132 + 11 x = 9.433981132 + 11 Combine like terms: 9.433981132 + 11 = 20.433981132 x = 20.433981132 Simplifying x = 20.433981132Subproblem 2
x + -11 = -9.433981132 Simplifying x + -11 = -9.433981132 Reorder the terms: -11 + x = -9.433981132 Solving -11 + x = -9.433981132 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 = -9.433981132 + 11 Combine like terms: -11 + 11 = 0 0 + x = -9.433981132 + 11 x = -9.433981132 + 11 Combine like terms: -9.433981132 + 11 = 1.566018868 x = 1.566018868 Simplifying x = 1.566018868Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.433981132, 1.566018868}
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