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Simplifying x2 + -23x + -3 = 0 Reorder the terms: -3 + -23x + x2 = 0 Solving -3 + -23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -23x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -23x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -23x + x2 = 0 + 3 -23x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -23x + x2 = 3 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 = 3 + 132.25 Reorder the terms: 132.25 + -23x + x2 = 3 + 132.25 Combine like terms: 3 + 132.25 = 135.25 132.25 + -23x + x2 = 135.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 135.25 Calculate the square root of the right side: 11.62970335 Break this problem into two subproblems by setting (x + -11.5) equal to 11.62970335 and -11.62970335.Subproblem 1
x + -11.5 = 11.62970335 Simplifying x + -11.5 = 11.62970335 Reorder the terms: -11.5 + x = 11.62970335 Solving -11.5 + x = 11.62970335 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 = 11.62970335 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 11.62970335 + 11.5 x = 11.62970335 + 11.5 Combine like terms: 11.62970335 + 11.5 = 23.12970335 x = 23.12970335 Simplifying x = 23.12970335Subproblem 2
x + -11.5 = -11.62970335 Simplifying x + -11.5 = -11.62970335 Reorder the terms: -11.5 + x = -11.62970335 Solving -11.5 + x = -11.62970335 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 = -11.62970335 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -11.62970335 + 11.5 x = -11.62970335 + 11.5 Combine like terms: -11.62970335 + 11.5 = -0.12970335 x = -0.12970335 Simplifying x = -0.12970335Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.12970335, -0.12970335}
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