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Simplifying -2x2 + 5x + 9 = 0 Reorder the terms: 9 + 5x + -2x2 = 0 Solving 9 + 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'. -4.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -2.5x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -2.5x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -2.5x + x2 = 0 + 4.5 -2.5x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -2.5x + x2 = 4.5 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 = 4.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 4.5 + 1.5625 Combine like terms: 4.5 + 1.5625 = 6.0625 1.5625 + -2.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + -1.25) equal to 2.46221445 and -2.46221445.Subproblem 1
x + -1.25 = 2.46221445 Simplifying x + -1.25 = 2.46221445 Reorder the terms: -1.25 + x = 2.46221445 Solving -1.25 + x = 2.46221445 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 = 2.46221445 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.46221445 + 1.25 x = 2.46221445 + 1.25 Combine like terms: 2.46221445 + 1.25 = 3.71221445 x = 3.71221445 Simplifying x = 3.71221445Subproblem 2
x + -1.25 = -2.46221445 Simplifying x + -1.25 = -2.46221445 Reorder the terms: -1.25 + x = -2.46221445 Solving -1.25 + x = -2.46221445 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 = -2.46221445 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.46221445 + 1.25 x = -2.46221445 + 1.25 Combine like terms: -2.46221445 + 1.25 = -1.21221445 x = -1.21221445 Simplifying x = -1.21221445Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.71221445, -1.21221445}
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