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Simplifying x2 + -23x + -130 = 0 Reorder the terms: -130 + -23x + x2 = 0 Solving -130 + -23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + -23x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + -23x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + -23x + x2 = 0 + 130 -23x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 -23x + x2 = 130 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 = 130 + 132.25 Reorder the terms: 132.25 + -23x + x2 = 130 + 132.25 Combine like terms: 130 + 132.25 = 262.25 132.25 + -23x + x2 = 262.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 262.25 Calculate the square root of the right side: 16.194134741 Break this problem into two subproblems by setting (x + -11.5) equal to 16.194134741 and -16.194134741.Subproblem 1
x + -11.5 = 16.194134741 Simplifying x + -11.5 = 16.194134741 Reorder the terms: -11.5 + x = 16.194134741 Solving -11.5 + x = 16.194134741 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 = 16.194134741 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 16.194134741 + 11.5 x = 16.194134741 + 11.5 Combine like terms: 16.194134741 + 11.5 = 27.694134741 x = 27.694134741 Simplifying x = 27.694134741Subproblem 2
x + -11.5 = -16.194134741 Simplifying x + -11.5 = -16.194134741 Reorder the terms: -11.5 + x = -16.194134741 Solving -11.5 + x = -16.194134741 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 = -16.194134741 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -16.194134741 + 11.5 x = -16.194134741 + 11.5 Combine like terms: -16.194134741 + 11.5 = -4.694134741 x = -4.694134741 Simplifying x = -4.694134741Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.694134741, -4.694134741}
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