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Simplifying 2x2 + 5x + -180 = 0 Reorder the terms: -180 + 5x + 2x2 = 0 Solving -180 + 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'. -90 + 2.5x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + 2.5x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 2.5x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 2.5x + x2 = 0 + 90 2.5x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 2.5x + x2 = 90 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 = 90 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 90 + 1.5625 Combine like terms: 90 + 1.5625 = 91.5625 1.5625 + 2.5x + x2 = 91.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 91.5625 Calculate the square root of the right side: 9.568829605 Break this problem into two subproblems by setting (x + 1.25) equal to 9.568829605 and -9.568829605.Subproblem 1
x + 1.25 = 9.568829605 Simplifying x + 1.25 = 9.568829605 Reorder the terms: 1.25 + x = 9.568829605 Solving 1.25 + x = 9.568829605 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 = 9.568829605 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 9.568829605 + -1.25 x = 9.568829605 + -1.25 Combine like terms: 9.568829605 + -1.25 = 8.318829605 x = 8.318829605 Simplifying x = 8.318829605Subproblem 2
x + 1.25 = -9.568829605 Simplifying x + 1.25 = -9.568829605 Reorder the terms: 1.25 + x = -9.568829605 Solving 1.25 + x = -9.568829605 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 = -9.568829605 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -9.568829605 + -1.25 x = -9.568829605 + -1.25 Combine like terms: -9.568829605 + -1.25 = -10.818829605 x = -10.818829605 Simplifying x = -10.818829605Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.318829605, -10.818829605}
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