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Simplifying -101 = x2 + -23x Reorder the terms: -101 = -23x + x2 Solving -101 = -23x + x2 Solving for variable 'x'. Reorder the terms: -101 + 23x + -1x2 = -23x + 23x + x2 + -1x2 Combine like terms: -23x + 23x = 0 -101 + 23x + -1x2 = 0 + x2 + -1x2 -101 + 23x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -101 + 23x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 101 + -23x + x2 = 0 Move the constant term to the right: Add '-101' to each side of the equation. 101 + -23x + -101 + x2 = 0 + -101 Reorder the terms: 101 + -101 + -23x + x2 = 0 + -101 Combine like terms: 101 + -101 = 0 0 + -23x + x2 = 0 + -101 -23x + x2 = 0 + -101 Combine like terms: 0 + -101 = -101 -23x + x2 = -101 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 = -101 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -101 + 132.25 Combine like terms: -101 + 132.25 = 31.25 132.25 + -23x + x2 = 31.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (x + -11.5) equal to 5.590169944 and -5.590169944.Subproblem 1
x + -11.5 = 5.590169944 Simplifying x + -11.5 = 5.590169944 Reorder the terms: -11.5 + x = 5.590169944 Solving -11.5 + x = 5.590169944 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 = 5.590169944 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 5.590169944 + 11.5 x = 5.590169944 + 11.5 Combine like terms: 5.590169944 + 11.5 = 17.090169944 x = 17.090169944 Simplifying x = 17.090169944Subproblem 2
x + -11.5 = -5.590169944 Simplifying x + -11.5 = -5.590169944 Reorder the terms: -11.5 + x = -5.590169944 Solving -11.5 + x = -5.590169944 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 = -5.590169944 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -5.590169944 + 11.5 x = -5.590169944 + 11.5 Combine like terms: -5.590169944 + 11.5 = 5.909830056 x = 5.909830056 Simplifying x = 5.909830056Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.090169944, 5.909830056}
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