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Simplifying -8x2 + 4x + 9 = 0 Reorder the terms: 9 + 4x + -8x2 = 0 Solving 9 + 4x + -8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.125 + -0.5x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -0.5x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -0.5x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -0.5x + x2 = 0 + 1.125 -0.5x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -0.5x + x2 = 1.125 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 = 1.125 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 1.125 + 0.0625 Combine like terms: 1.125 + 0.0625 = 1.1875 0.0625 + -0.5x + x2 = 1.1875 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 1.1875 Calculate the square root of the right side: 1.089724736 Break this problem into two subproblems by setting (x + -0.25) equal to 1.089724736 and -1.089724736.Subproblem 1
x + -0.25 = 1.089724736 Simplifying x + -0.25 = 1.089724736 Reorder the terms: -0.25 + x = 1.089724736 Solving -0.25 + x = 1.089724736 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 = 1.089724736 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.089724736 + 0.25 x = 1.089724736 + 0.25 Combine like terms: 1.089724736 + 0.25 = 1.339724736 x = 1.339724736 Simplifying x = 1.339724736Subproblem 2
x + -0.25 = -1.089724736 Simplifying x + -0.25 = -1.089724736 Reorder the terms: -0.25 + x = -1.089724736 Solving -0.25 + x = -1.089724736 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 = -1.089724736 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.089724736 + 0.25 x = -1.089724736 + 0.25 Combine like terms: -1.089724736 + 0.25 = -0.839724736 x = -0.839724736 Simplifying x = -0.839724736Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.339724736, -0.839724736}
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