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Simplifying (48x4) + -1(6x2) + -1 = 0 Remove parenthesis around (6x2) (48x4) + -1 * 6x2 + -1 = 0 Multiply -1 * 6 (48x4) + -6x2 + -1 = 0 Reorder the terms: -1 + -6x2 + (48x4) = 0 Solving -1 + -6x2 + (48x4) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.02083333333 + -0.125x2 + x4 = 0 Move the constant term to the right: Add '0.02083333333' to each side of the equation. -0.02083333333 + -0.125x2 + 0.02083333333 + x4 = 0 + 0.02083333333 Reorder the terms: -0.02083333333 + 0.02083333333 + -0.125x2 + x4 = 0 + 0.02083333333 Combine like terms: -0.02083333333 + 0.02083333333 = 0.00000000000 0.00000000000 + -0.125x2 + x4 = 0 + 0.02083333333 -0.125x2 + x4 = 0 + 0.02083333333 Combine like terms: 0 + 0.02083333333 = 0.02083333333 -0.125x2 + x4 = 0.02083333333 The x term is -0.125x2. 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. -0.125x2 + 0.00390625 + x4 = 0.02083333333 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x2 + x4 = 0.02083333333 + 0.00390625 Combine like terms: 0.02083333333 + 0.00390625 = 0.02473958333 0.00390625 + -0.125x2 + x4 = 0.02473958333 Factor a perfect square on the left side: ((x2) + -0.0625)((x2) + -0.0625) = 0.02473958333 Calculate the square root of the right side: 0.157288217 Break this problem into two subproblems by setting ((x2) + -0.0625) equal to 0.157288217 and -0.157288217.Subproblem 1
(x2) + -0.0625 = 0.157288217 Simplifying (x2) + -0.0625 = 0.157288217 x2 + -0.0625 = 0.157288217 Reorder the terms: -0.0625 + x2 = 0.157288217 Solving -0.0625 + x2 = 0.157288217 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 + x2 = 0.157288217 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x2 = 0.157288217 + 0.0625 x2 = 0.157288217 + 0.0625 Combine like terms: 0.157288217 + 0.0625 = 0.219788217 x2 = 0.219788217 Simplifying x2 = 0.219788217 Take the square root of each side: x = {-0.46881576, 0.46881576}Subproblem 2
(x2) + -0.0625 = -0.157288217 Simplifying (x2) + -0.0625 = -0.157288217 x2 + -0.0625 = -0.157288217 Reorder the terms: -0.0625 + x2 = -0.157288217 Solving -0.0625 + x2 = -0.157288217 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 + x2 = -0.157288217 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x2 = -0.157288217 + 0.0625 x2 = -0.157288217 + 0.0625 Combine like terms: -0.157288217 + 0.0625 = -0.094788217 x2 = -0.094788217 Simplifying x2 = -0.094788217 Reorder the terms: 0.094788217 + x2 = -0.094788217 + 0.094788217 Combine like terms: -0.094788217 + 0.094788217 = 0.000000000 0.094788217 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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