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Simplifying -8x2 + 9x + 9 = 0 Reorder the terms: 9 + 9x + -8x2 = 0 Solving 9 + 9x + -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 + -1.125x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -1.125x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -1.125x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -1.125x + x2 = 0 + 1.125 -1.125x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -1.125x + x2 = 1.125 The x term is -1.125x. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125x + 0.31640625 + x2 = 1.125 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = 1.125 + 0.31640625 Combine like terms: 1.125 + 0.31640625 = 1.44140625 0.31640625 + -1.125x + x2 = 1.44140625 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 1.44140625 Calculate the square root of the right side: 1.200585795 Break this problem into two subproblems by setting (x + -0.5625) equal to 1.200585795 and -1.200585795.Subproblem 1
x + -0.5625 = 1.200585795 Simplifying x + -0.5625 = 1.200585795 Reorder the terms: -0.5625 + x = 1.200585795 Solving -0.5625 + x = 1.200585795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = 1.200585795 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 1.200585795 + 0.5625 x = 1.200585795 + 0.5625 Combine like terms: 1.200585795 + 0.5625 = 1.763085795 x = 1.763085795 Simplifying x = 1.763085795Subproblem 2
x + -0.5625 = -1.200585795 Simplifying x + -0.5625 = -1.200585795 Reorder the terms: -0.5625 + x = -1.200585795 Solving -0.5625 + x = -1.200585795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = -1.200585795 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -1.200585795 + 0.5625 x = -1.200585795 + 0.5625 Combine like terms: -1.200585795 + 0.5625 = -0.638085795 x = -0.638085795 Simplifying x = -0.638085795Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.763085795, -0.638085795}
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