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Simplifying x2 + -23x = 9 Reorder the terms: -23x + x2 = 9 Solving -23x + x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -23x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -23x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -23x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -23x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -23x + x2 = 0 + 9 -23x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -23x + x2 = 9 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 = 9 + 132.25 Reorder the terms: 132.25 + -23x + x2 = 9 + 132.25 Combine like terms: 9 + 132.25 = 141.25 132.25 + -23x + x2 = 141.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 141.25 Calculate the square root of the right side: 11.884864324 Break this problem into two subproblems by setting (x + -11.5) equal to 11.884864324 and -11.884864324.Subproblem 1
x + -11.5 = 11.884864324 Simplifying x + -11.5 = 11.884864324 Reorder the terms: -11.5 + x = 11.884864324 Solving -11.5 + x = 11.884864324 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 = 11.884864324 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 11.884864324 + 11.5 x = 11.884864324 + 11.5 Combine like terms: 11.884864324 + 11.5 = 23.384864324 x = 23.384864324 Simplifying x = 23.384864324Subproblem 2
x + -11.5 = -11.884864324 Simplifying x + -11.5 = -11.884864324 Reorder the terms: -11.5 + x = -11.884864324 Solving -11.5 + x = -11.884864324 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 = -11.884864324 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -11.884864324 + 11.5 x = -11.884864324 + 11.5 Combine like terms: -11.884864324 + 11.5 = -0.384864324 x = -0.384864324 Simplifying x = -0.384864324Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.384864324, -0.384864324}
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