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Simplifying x2 + 23x + -90 = 0 Reorder the terms: -90 + 23x + x2 = 0 Solving -90 + 23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 23x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 23x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 23x + x2 = 0 + 90 23x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 23x + x2 = 90 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 = 90 + 132.25 Reorder the terms: 132.25 + 23x + x2 = 90 + 132.25 Combine like terms: 90 + 132.25 = 222.25 132.25 + 23x + x2 = 222.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 222.25 Calculate the square root of the right side: 14.908051516 Break this problem into two subproblems by setting (x + 11.5) equal to 14.908051516 and -14.908051516.Subproblem 1
x + 11.5 = 14.908051516 Simplifying x + 11.5 = 14.908051516 Reorder the terms: 11.5 + x = 14.908051516 Solving 11.5 + x = 14.908051516 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 = 14.908051516 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 14.908051516 + -11.5 x = 14.908051516 + -11.5 Combine like terms: 14.908051516 + -11.5 = 3.408051516 x = 3.408051516 Simplifying x = 3.408051516Subproblem 2
x + 11.5 = -14.908051516 Simplifying x + 11.5 = -14.908051516 Reorder the terms: 11.5 + x = -14.908051516 Solving 11.5 + x = -14.908051516 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 = -14.908051516 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -14.908051516 + -11.5 x = -14.908051516 + -11.5 Combine like terms: -14.908051516 + -11.5 = -26.408051516 x = -26.408051516 Simplifying x = -26.408051516Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.408051516, -26.408051516}
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