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Simplifying 0 = -8x2 + 2x + 9 Reorder the terms: 0 = 9 + 2x + -8x2 Solving 0 = 9 + 2x + -8x2 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + -2x + 8x2 = 9 + 2x + -8x2 + -9 + -2x + 8x2 Reorder the terms: -9 + -2x + 8x2 = 9 + -9 + 2x + -2x + -8x2 + 8x2 Combine like terms: 9 + -9 = 0 -9 + -2x + 8x2 = 0 + 2x + -2x + -8x2 + 8x2 -9 + -2x + 8x2 = 2x + -2x + -8x2 + 8x2 Combine like terms: 2x + -2x = 0 -9 + -2x + 8x2 = 0 + -8x2 + 8x2 -9 + -2x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 -9 + -2x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + -0.25x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -0.25x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -0.25x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -0.25x + x2 = 0 + 1.125 -0.25x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -0.25x + x2 = 1.125 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 1.125 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 1.125 + 0.015625 Combine like terms: 1.125 + 0.015625 = 1.140625 0.015625 + -0.25x + x2 = 1.140625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (x + -0.125) equal to 1.068000468 and -1.068000468.Subproblem 1
x + -0.125 = 1.068000468 Simplifying x + -0.125 = 1.068000468 Reorder the terms: -0.125 + x = 1.068000468 Solving -0.125 + x = 1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 1.068000468 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 1.068000468 + 0.125 x = 1.068000468 + 0.125 Combine like terms: 1.068000468 + 0.125 = 1.193000468 x = 1.193000468 Simplifying x = 1.193000468Subproblem 2
x + -0.125 = -1.068000468 Simplifying x + -0.125 = -1.068000468 Reorder the terms: -0.125 + x = -1.068000468 Solving -0.125 + x = -1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -1.068000468 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -1.068000468 + 0.125 x = -1.068000468 + 0.125 Combine like terms: -1.068000468 + 0.125 = -0.943000468 x = -0.943000468 Simplifying x = -0.943000468Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.193000468, -0.943000468}
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