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Simplifying 15x4 + -15x2 = 4 Reorder the terms: -15x2 + 15x4 = 4 Solving -15x2 + 15x4 = 4 Solving for variable 'x'. Reorder the terms: -4 + -15x2 + 15x4 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -15x2 + 15x4 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.2666666667 + -1x2 + x4 = 0 Move the constant term to the right: Add '0.2666666667' to each side of the equation. -0.2666666667 + -1x2 + 0.2666666667 + x4 = 0 + 0.2666666667 Reorder the terms: -0.2666666667 + 0.2666666667 + -1x2 + x4 = 0 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + -1x2 + x4 = 0 + 0.2666666667 -1x2 + x4 = 0 + 0.2666666667 Combine like terms: 0 + 0.2666666667 = 0.2666666667 -1x2 + x4 = 0.2666666667 The x term is -1x2. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x2 + 0.25 + x4 = 0.2666666667 + 0.25 Reorder the terms: 0.25 + -1x2 + x4 = 0.2666666667 + 0.25 Combine like terms: 0.2666666667 + 0.25 = 0.5166666667 0.25 + -1x2 + x4 = 0.5166666667 Factor a perfect square on the left side: (x2 + -0.5)(x2 + -0.5) = 0.5166666667 Calculate the square root of the right side: 0.718795288 Break this problem into two subproblems by setting (x2 + -0.5) equal to 0.718795288 and -0.718795288.Subproblem 1
x2 + -0.5 = 0.718795288 Simplifying x2 + -0.5 = 0.718795288 Reorder the terms: -0.5 + x2 = 0.718795288 Solving -0.5 + x2 = 0.718795288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = 0.718795288 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 0.718795288 + 0.5 x2 = 0.718795288 + 0.5 Combine like terms: 0.718795288 + 0.5 = 1.218795288 x2 = 1.218795288 Simplifying x2 = 1.218795288 Take the square root of each side: x = {-1.10399062, 1.10399062}Subproblem 2
x2 + -0.5 = -0.718795288 Simplifying x2 + -0.5 = -0.718795288 Reorder the terms: -0.5 + x2 = -0.718795288 Solving -0.5 + x2 = -0.718795288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = -0.718795288 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -0.718795288 + 0.5 x2 = -0.718795288 + 0.5 Combine like terms: -0.718795288 + 0.5 = -0.218795288 x2 = -0.218795288 Simplifying x2 = -0.218795288 Reorder the terms: 0.218795288 + x2 = -0.218795288 + 0.218795288 Combine like terms: -0.218795288 + 0.218795288 = 0.000000000 0.218795288 + 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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