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Simplifying x2 + 19x + -50 = 0 Reorder the terms: -50 + 19x + x2 = 0 Solving -50 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 19x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 19x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 19x + x2 = 0 + 50 19x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 19x + x2 = 50 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = 50 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 50 + 90.25 Combine like terms: 50 + 90.25 = 140.25 90.25 + 19x + x2 = 140.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 140.25 Calculate the square root of the right side: 11.842719282 Break this problem into two subproblems by setting (x + 9.5) equal to 11.842719282 and -11.842719282.Subproblem 1
x + 9.5 = 11.842719282 Simplifying x + 9.5 = 11.842719282 Reorder the terms: 9.5 + x = 11.842719282 Solving 9.5 + x = 11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 11.842719282 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 11.842719282 + -9.5 x = 11.842719282 + -9.5 Combine like terms: 11.842719282 + -9.5 = 2.342719282 x = 2.342719282 Simplifying x = 2.342719282Subproblem 2
x + 9.5 = -11.842719282 Simplifying x + 9.5 = -11.842719282 Reorder the terms: 9.5 + x = -11.842719282 Solving 9.5 + x = -11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -11.842719282 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -11.842719282 + -9.5 x = -11.842719282 + -9.5 Combine like terms: -11.842719282 + -9.5 = -21.342719282 x = -21.342719282 Simplifying x = -21.342719282Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.342719282, -21.342719282}
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