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Simplifying x2 + 23x + -72 = 0 Reorder the terms: -72 + 23x + x2 = 0 Solving -72 + 23x + x2 = 0 Solving for variable 'x'. 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 = 2.791605928 x = 2.791605928 Simplifying x = 2.791605928Subproblem 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 = -25.791605928 x = -25.791605928 Simplifying x = -25.791605928Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.791605928, -25.791605928}
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