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Simplifying x2 + -23x = 72 Reorder the terms: -23x + x2 = 72 Solving -23x + x2 = 72 Solving for variable 'x'. Reorder the terms: -72 + -23x + x2 = 72 + -72 Combine like terms: 72 + -72 = 0 -72 + -23x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -23x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + -23x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -23x + x2 = 0 + 72 -23x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 -23x + x2 = 72 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 = 72 + 132.25 Reorder the terms: 132.25 + -23x + x2 = 72 + 132.25 Combine like terms: 72 + 132.25 = 204.25 132.25 + -23x + x2 = 204.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 204.25 Calculate the square root of the right side: 14.291605928 Break this problem into two subproblems by setting (x + -11.5) equal to 14.291605928 and -14.291605928.Subproblem 1
x + -11.5 = 14.291605928 Simplifying x + -11.5 = 14.291605928 Reorder the terms: -11.5 + x = 14.291605928 Solving -11.5 + x = 14.291605928 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 = 14.291605928 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 14.291605928 + 11.5 x = 14.291605928 + 11.5 Combine like terms: 14.291605928 + 11.5 = 25.791605928 x = 25.791605928 Simplifying x = 25.791605928Subproblem 2
x + -11.5 = -14.291605928 Simplifying x + -11.5 = -14.291605928 Reorder the terms: -11.5 + x = -14.291605928 Solving -11.5 + x = -14.291605928 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 = -14.291605928 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -14.291605928 + 11.5 x = -14.291605928 + 11.5 Combine like terms: -14.291605928 + 11.5 = -2.791605928 x = -2.791605928 Simplifying x = -2.791605928Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.791605928, -2.791605928}
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