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Simplifying x2 + -23x + -65 = 0 Reorder the terms: -65 + -23x + x2 = 0 Solving -65 + -23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + -23x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + -23x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + -23x + x2 = 0 + 65 -23x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 -23x + x2 = 65 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 = 65 + 132.25 Reorder the terms: 132.25 + -23x + x2 = 65 + 132.25 Combine like terms: 65 + 132.25 = 197.25 132.25 + -23x + x2 = 197.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 197.25 Calculate the square root of the right side: 14.044571905 Break this problem into two subproblems by setting (x + -11.5) equal to 14.044571905 and -14.044571905.Subproblem 1
x + -11.5 = 14.044571905 Simplifying x + -11.5 = 14.044571905 Reorder the terms: -11.5 + x = 14.044571905 Solving -11.5 + x = 14.044571905 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 = 14.044571905 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 14.044571905 + 11.5 x = 14.044571905 + 11.5 Combine like terms: 14.044571905 + 11.5 = 25.544571905 x = 25.544571905 Simplifying x = 25.544571905Subproblem 2
x + -11.5 = -14.044571905 Simplifying x + -11.5 = -14.044571905 Reorder the terms: -11.5 + x = -14.044571905 Solving -11.5 + x = -14.044571905 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 = -14.044571905 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -14.044571905 + 11.5 x = -14.044571905 + 11.5 Combine like terms: -14.044571905 + 11.5 = -2.544571905 x = -2.544571905 Simplifying x = -2.544571905Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.544571905, -2.544571905}
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