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Simplifying x2 + -23x = -32 Reorder the terms: -23x + x2 = -32 Solving -23x + x2 = -32 Solving for variable 'x'. Reorder the terms: 32 + -23x + x2 = -32 + 32 Combine like terms: -32 + 32 = 0 32 + -23x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -23x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + -23x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -23x + x2 = 0 + -32 -23x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 -23x + x2 = -32 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = -32 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -32 + 132.25 Combine like terms: -32 + 132.25 = 100.25 132.25 + -23x + x2 = 100.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (x + -11.5) equal to 10.012492197 and -10.012492197.Subproblem 1
x + -11.5 = 10.012492197 Simplifying x + -11.5 = 10.012492197 Reorder the terms: -11.5 + x = 10.012492197 Solving -11.5 + x = 10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 10.012492197 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 10.012492197 + 11.5 x = 10.012492197 + 11.5 Combine like terms: 10.012492197 + 11.5 = 21.512492197 x = 21.512492197 Simplifying x = 21.512492197Subproblem 2
x + -11.5 = -10.012492197 Simplifying x + -11.5 = -10.012492197 Reorder the terms: -11.5 + x = -10.012492197 Solving -11.5 + x = -10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -10.012492197 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -10.012492197 + 11.5 x = -10.012492197 + 11.5 Combine like terms: -10.012492197 + 11.5 = 1.487507803 x = 1.487507803 Simplifying x = 1.487507803Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.512492197, 1.487507803}
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