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Simplifying (2x2 + 4) + -1[-8 + 2(7 + -3x2) + x] = 0 Reorder the terms: (4 + 2x2) + -1[-8 + 2(7 + -3x2) + x] = 0 Remove parenthesis around (4 + 2x2) 4 + 2x2 + -1[-8 + 2(7 + -3x2) + x] = 0 4 + 2x2 + -1[-8 + (7 * 2 + -3x2 * 2) + x] = 0 4 + 2x2 + -1[-8 + (14 + -6x2) + x] = 0 Reorder the terms: 4 + 2x2 + -1[-8 + 14 + x + -6x2] = 0 Combine like terms: -8 + 14 = 6 4 + 2x2 + -1[6 + x + -6x2] = 0 4 + 2x2 + [6 * -1 + x * -1 + -6x2 * -1] = 0 4 + 2x2 + [-6 + -1x + 6x2] = 0 Reorder the terms: 4 + -6 + -1x + 2x2 + 6x2 = 0 Combine like terms: 4 + -6 = -2 -2 + -1x + 2x2 + 6x2 = 0 Combine like terms: 2x2 + 6x2 = 8x2 -2 + -1x + 8x2 = 0 Solving -2 + -1x + 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'. -0.25 + -0.125x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.125x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.125x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.125x + x2 = 0 + 0.25 -0.125x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.125x + x2 = 0.25 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 = 0.25 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 0.25 + 0.00390625 Combine like terms: 0.25 + 0.00390625 = 0.25390625 0.00390625 + -0.125x + x2 = 0.25390625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 0.25390625 Calculate the square root of the right side: 0.503891109 Break this problem into two subproblems by setting (x + -0.0625) equal to 0.503891109 and -0.503891109.Subproblem 1
x + -0.0625 = 0.503891109 Simplifying x + -0.0625 = 0.503891109 Reorder the terms: -0.0625 + x = 0.503891109 Solving -0.0625 + x = 0.503891109 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 = 0.503891109 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 0.503891109 + 0.0625 x = 0.503891109 + 0.0625 Combine like terms: 0.503891109 + 0.0625 = 0.566391109 x = 0.566391109 Simplifying x = 0.566391109Subproblem 2
x + -0.0625 = -0.503891109 Simplifying x + -0.0625 = -0.503891109 Reorder the terms: -0.0625 + x = -0.503891109 Solving -0.0625 + x = -0.503891109 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 = -0.503891109 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -0.503891109 + 0.0625 x = -0.503891109 + 0.0625 Combine like terms: -0.503891109 + 0.0625 = -0.441391109 x = -0.441391109 Simplifying x = -0.441391109Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.566391109, -0.441391109}
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