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Simplifying 0 = -8x2 + 9x + 7 Reorder the terms: 0 = 7 + 9x + -8x2 Solving 0 = 7 + 9x + -8x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + -9x + 8x2 = 7 + 9x + -8x2 + -7 + -9x + 8x2 Reorder the terms: -7 + -9x + 8x2 = 7 + -7 + 9x + -9x + -8x2 + 8x2 Combine like terms: 7 + -7 = 0 -7 + -9x + 8x2 = 0 + 9x + -9x + -8x2 + 8x2 -7 + -9x + 8x2 = 9x + -9x + -8x2 + 8x2 Combine like terms: 9x + -9x = 0 -7 + -9x + 8x2 = 0 + -8x2 + 8x2 -7 + -9x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 -7 + -9x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + -1.125x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -1.125x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -1.125x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -1.125x + x2 = 0 + 0.875 -1.125x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -1.125x + x2 = 0.875 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 = 0.875 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = 0.875 + 0.31640625 Combine like terms: 0.875 + 0.31640625 = 1.19140625 0.31640625 + -1.125x + x2 = 1.19140625 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 1.19140625 Calculate the square root of the right side: 1.091515575 Break this problem into two subproblems by setting (x + -0.5625) equal to 1.091515575 and -1.091515575.Subproblem 1
x + -0.5625 = 1.091515575 Simplifying x + -0.5625 = 1.091515575 Reorder the terms: -0.5625 + x = 1.091515575 Solving -0.5625 + x = 1.091515575 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 = 1.091515575 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 1.091515575 + 0.5625 x = 1.091515575 + 0.5625 Combine like terms: 1.091515575 + 0.5625 = 1.654015575 x = 1.654015575 Simplifying x = 1.654015575Subproblem 2
x + -0.5625 = -1.091515575 Simplifying x + -0.5625 = -1.091515575 Reorder the terms: -0.5625 + x = -1.091515575 Solving -0.5625 + x = -1.091515575 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 = -1.091515575 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -1.091515575 + 0.5625 x = -1.091515575 + 0.5625 Combine like terms: -1.091515575 + 0.5625 = -0.529015575 x = -0.529015575 Simplifying x = -0.529015575Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.654015575, -0.529015575}
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