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Simplifying (2x2) + 5x + -8 = 0 Reorder the terms: -8 + 5x + (2x2) = 0 Solving -8 + 5x + (2x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + 2.5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 2.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 2.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2.5x + x2 = 0 + 4 2.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 2.5x + x2 = 4 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 4 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 4 + 1.5625 Combine like terms: 4 + 1.5625 = 5.5625 1.5625 + 2.5x + x2 = 5.5625 Factor a perfect square on the left side: ((x) + 1.25)((x) + 1.25) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting ((x) + 1.25) equal to 2.358495283 and -2.358495283.Subproblem 1
(x) + 1.25 = 2.358495283 Simplifying (x) + 1.25 = 2.358495283 x + 1.25 = 2.358495283 Reorder the terms: 1.25 + x = 2.358495283 Solving 1.25 + x = 2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.358495283 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.358495283 + -1.25 x = 2.358495283 + -1.25 Combine like terms: 2.358495283 + -1.25 = 1.108495283 x = 1.108495283 Simplifying x = 1.108495283Subproblem 2
(x) + 1.25 = -2.358495283 Simplifying (x) + 1.25 = -2.358495283 x + 1.25 = -2.358495283 Reorder the terms: 1.25 + x = -2.358495283 Solving 1.25 + x = -2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.358495283 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.358495283 + -1.25 x = -2.358495283 + -1.25 Combine like terms: -2.358495283 + -1.25 = -3.608495283 x = -3.608495283 Simplifying x = -3.608495283Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.108495283, -3.608495283}
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