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Simplifying 2x2 + 5x + -4 = 180 Reorder the terms: -4 + 5x + 2x2 = 180 Solving -4 + 5x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -4 + -180 + 5x + 2x2 = 180 + -180 Combine like terms: -4 + -180 = -184 -184 + 5x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -184 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -92 + 2.5x + x2 = 0 Move the constant term to the right: Add '92' to each side of the equation. -92 + 2.5x + 92 + x2 = 0 + 92 Reorder the terms: -92 + 92 + 2.5x + x2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + 2.5x + x2 = 0 + 92 2.5x + x2 = 0 + 92 Combine like terms: 0 + 92 = 92 2.5x + x2 = 92 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 = 92 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 92 + 1.5625 Combine like terms: 92 + 1.5625 = 93.5625 1.5625 + 2.5x + x2 = 93.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 93.5625 Calculate the square root of the right side: 9.672771061 Break this problem into two subproblems by setting (x + 1.25) equal to 9.672771061 and -9.672771061.Subproblem 1
x + 1.25 = 9.672771061 Simplifying x + 1.25 = 9.672771061 Reorder the terms: 1.25 + x = 9.672771061 Solving 1.25 + x = 9.672771061 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 = 9.672771061 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 9.672771061 + -1.25 x = 9.672771061 + -1.25 Combine like terms: 9.672771061 + -1.25 = 8.422771061 x = 8.422771061 Simplifying x = 8.422771061Subproblem 2
x + 1.25 = -9.672771061 Simplifying x + 1.25 = -9.672771061 Reorder the terms: 1.25 + x = -9.672771061 Solving 1.25 + x = -9.672771061 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 = -9.672771061 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -9.672771061 + -1.25 x = -9.672771061 + -1.25 Combine like terms: -9.672771061 + -1.25 = -10.922771061 x = -10.922771061 Simplifying x = -10.922771061Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.422771061, -10.922771061}
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