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Simplifying x2 + -13x + -90 = 8 Reorder the terms: -90 + -13x + x2 = 8 Solving -90 + -13x + x2 = 8 Solving for variable 'x'. Reorder the terms: -90 + -8 + -13x + x2 = 8 + -8 Combine like terms: -90 + -8 = -98 -98 + -13x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -98 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + -13x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + -13x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + -13x + x2 = 0 + 98 -13x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 -13x + x2 = 98 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 98 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 98 + 42.25 Combine like terms: 98 + 42.25 = 140.25 42.25 + -13x + x2 = 140.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 140.25 Calculate the square root of the right side: 11.842719282 Break this problem into two subproblems by setting (x + -6.5) equal to 11.842719282 and -11.842719282.Subproblem 1
x + -6.5 = 11.842719282 Simplifying x + -6.5 = 11.842719282 Reorder the terms: -6.5 + x = 11.842719282 Solving -6.5 + x = 11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 11.842719282 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 11.842719282 + 6.5 x = 11.842719282 + 6.5 Combine like terms: 11.842719282 + 6.5 = 18.342719282 x = 18.342719282 Simplifying x = 18.342719282Subproblem 2
x + -6.5 = -11.842719282 Simplifying x + -6.5 = -11.842719282 Reorder the terms: -6.5 + x = -11.842719282 Solving -6.5 + x = -11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -11.842719282 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -11.842719282 + 6.5 x = -11.842719282 + 6.5 Combine like terms: -11.842719282 + 6.5 = -5.342719282 x = -5.342719282 Simplifying x = -5.342719282Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.342719282, -5.342719282}
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