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Simplifying 8x2 = 18 + x Solving 8x2 = 18 + x Solving for variable 'x'. Reorder the terms: -18 + -1x + 8x2 = 18 + x + -18 + -1x Reorder the terms: -18 + -1x + 8x2 = 18 + -18 + x + -1x Combine like terms: 18 + -18 = 0 -18 + -1x + 8x2 = 0 + x + -1x -18 + -1x + 8x2 = x + -1x Combine like terms: x + -1x = 0 -18 + -1x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.25 + -0.125x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -0.125x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -0.125x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -0.125x + x2 = 0 + 2.25 -0.125x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -0.125x + x2 = 2.25 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = 2.25 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 2.25 + 0.00390625 Combine like terms: 2.25 + 0.00390625 = 2.25390625 0.00390625 + -0.125x + x2 = 2.25390625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 2.25390625 Calculate the square root of the right side: 1.501301519 Break this problem into two subproblems by setting (x + -0.0625) equal to 1.501301519 and -1.501301519.Subproblem 1
x + -0.0625 = 1.501301519 Simplifying x + -0.0625 = 1.501301519 Reorder the terms: -0.0625 + x = 1.501301519 Solving -0.0625 + x = 1.501301519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 1.501301519 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 1.501301519 + 0.0625 x = 1.501301519 + 0.0625 Combine like terms: 1.501301519 + 0.0625 = 1.563801519 x = 1.563801519 Simplifying x = 1.563801519Subproblem 2
x + -0.0625 = -1.501301519 Simplifying x + -0.0625 = -1.501301519 Reorder the terms: -0.0625 + x = -1.501301519 Solving -0.0625 + x = -1.501301519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -1.501301519 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -1.501301519 + 0.0625 x = -1.501301519 + 0.0625 Combine like terms: -1.501301519 + 0.0625 = -1.438801519 x = -1.438801519 Simplifying x = -1.438801519Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.563801519, -1.438801519}
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