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Simplifying x2 + -23x + -76 = 0 Reorder the terms: -76 + -23x + x2 = 0 Solving -76 + -23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + -23x + 76 + x2 = 0 + 76 Reorder the terms: -76 + 76 + -23x + x2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + -23x + x2 = 0 + 76 -23x + x2 = 0 + 76 Combine like terms: 0 + 76 = 76 -23x + x2 = 76 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 = 76 + 132.25 Reorder the terms: 132.25 + -23x + x2 = 76 + 132.25 Combine like terms: 76 + 132.25 = 208.25 132.25 + -23x + x2 = 208.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 208.25 Calculate the square root of the right side: 14.43086969 Break this problem into two subproblems by setting (x + -11.5) equal to 14.43086969 and -14.43086969.Subproblem 1
x + -11.5 = 14.43086969 Simplifying x + -11.5 = 14.43086969 Reorder the terms: -11.5 + x = 14.43086969 Solving -11.5 + x = 14.43086969 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 = 14.43086969 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 14.43086969 + 11.5 x = 14.43086969 + 11.5 Combine like terms: 14.43086969 + 11.5 = 25.93086969 x = 25.93086969 Simplifying x = 25.93086969Subproblem 2
x + -11.5 = -14.43086969 Simplifying x + -11.5 = -14.43086969 Reorder the terms: -11.5 + x = -14.43086969 Solving -11.5 + x = -14.43086969 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 = -14.43086969 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -14.43086969 + 11.5 x = -14.43086969 + 11.5 Combine like terms: -14.43086969 + 11.5 = -2.93086969 x = -2.93086969 Simplifying x = -2.93086969Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.93086969, -2.93086969}
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