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Simplifying 2x2 + -1x + -180 = 0 Reorder the terms: -180 + -1x + 2x2 = 0 Solving -180 + -1x + 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 + -0.5x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + -0.5x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -0.5x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -0.5x + x2 = 0 + 90 -0.5x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -0.5x + x2 = 90 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 90 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 90 + 0.0625 Combine like terms: 90 + 0.0625 = 90.0625 0.0625 + -0.5x + x2 = 90.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 90.0625 Calculate the square root of the right side: 9.490126448 Break this problem into two subproblems by setting (x + -0.25) equal to 9.490126448 and -9.490126448.Subproblem 1
x + -0.25 = 9.490126448 Simplifying x + -0.25 = 9.490126448 Reorder the terms: -0.25 + x = 9.490126448 Solving -0.25 + x = 9.490126448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 9.490126448 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 9.490126448 + 0.25 x = 9.490126448 + 0.25 Combine like terms: 9.490126448 + 0.25 = 9.740126448 x = 9.740126448 Simplifying x = 9.740126448Subproblem 2
x + -0.25 = -9.490126448 Simplifying x + -0.25 = -9.490126448 Reorder the terms: -0.25 + x = -9.490126448 Solving -0.25 + x = -9.490126448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -9.490126448 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -9.490126448 + 0.25 x = -9.490126448 + 0.25 Combine like terms: -9.490126448 + 0.25 = -9.240126448 x = -9.240126448 Simplifying x = -9.240126448Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.740126448, -9.240126448}
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