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Simplifying 2x2 + -9x + -2 = 0 Reorder the terms: -2 + -9x + 2x2 = 0 Solving -2 + -9x + 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'. -1 + -4.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -4.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -4.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4.5x + x2 = 0 + 1 -4.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -4.5x + x2 = 1 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 1 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 1 + 5.0625 Combine like terms: 1 + 5.0625 = 6.0625 5.0625 + -4.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + -2.25) equal to 2.46221445 and -2.46221445.Subproblem 1
x + -2.25 = 2.46221445 Simplifying x + -2.25 = 2.46221445 Reorder the terms: -2.25 + x = 2.46221445 Solving -2.25 + x = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 2.46221445 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.46221445 + 2.25 x = 2.46221445 + 2.25 Combine like terms: 2.46221445 + 2.25 = 4.71221445 x = 4.71221445 Simplifying x = 4.71221445Subproblem 2
x + -2.25 = -2.46221445 Simplifying x + -2.25 = -2.46221445 Reorder the terms: -2.25 + x = -2.46221445 Solving -2.25 + x = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -2.46221445 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.46221445 + 2.25 x = -2.46221445 + 2.25 Combine like terms: -2.46221445 + 2.25 = -0.21221445 x = -0.21221445 Simplifying x = -0.21221445Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.71221445, -0.21221445}
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