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Simplifying 0 = (x4) + -1(2(x2)) + -5 0 = x4 + -1(2(x2)) + -5 Remove parenthesis around (2x2) 0 = x4 + -1 * 2x2 + -5 Multiply -1 * 2 0 = x4 + -2x2 + -5 Reorder the terms: 0 = -5 + -2x2 + x4 Solving 0 = -5 + -2x2 + x4 Solving for variable 'x'. Combine like terms: 0 + 5 = 5 5 + 2x2 + -1x4 = -5 + -2x2 + x4 + 5 + 2x2 + -1x4 Reorder the terms: 5 + 2x2 + -1x4 = -5 + 5 + -2x2 + 2x2 + x4 + -1x4 Combine like terms: -5 + 5 = 0 5 + 2x2 + -1x4 = 0 + -2x2 + 2x2 + x4 + -1x4 5 + 2x2 + -1x4 = -2x2 + 2x2 + x4 + -1x4 Combine like terms: -2x2 + 2x2 = 0 5 + 2x2 + -1x4 = 0 + x4 + -1x4 5 + 2x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 5 + 2x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -2x2 + x4 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -2x2 + 5 + x4 = 0 + 5 Reorder the terms: -5 + 5 + -2x2 + x4 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x2 + x4 = 0 + 5 -2x2 + x4 = 0 + 5 Combine like terms: 0 + 5 = 5 -2x2 + x4 = 5 The x term is -2x2. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x2 + 1 + x4 = 5 + 1 Reorder the terms: 1 + -2x2 + x4 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + -2x2 + x4 = 6 Factor a perfect square on the left side: (x2 + -1)(x2 + -1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x2 + -1) equal to 2.449489743 and -2.449489743.Subproblem 1
x2 + -1 = 2.449489743 Simplifying x2 + -1 = 2.449489743 Reorder the terms: -1 + x2 = 2.449489743 Solving -1 + x2 = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = 2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = 2.449489743 + 1 x2 = 2.449489743 + 1 Combine like terms: 2.449489743 + 1 = 3.449489743 x2 = 3.449489743 Simplifying x2 = 3.449489743 Take the square root of each side: x = {-1.8572802, 1.8572802}Subproblem 2
x2 + -1 = -2.449489743 Simplifying x2 + -1 = -2.449489743 Reorder the terms: -1 + x2 = -2.449489743 Solving -1 + x2 = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = -2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = -2.449489743 + 1 x2 = -2.449489743 + 1 Combine like terms: -2.449489743 + 1 = -1.449489743 x2 = -1.449489743 Simplifying x2 = -1.449489743 Reorder the terms: 1.449489743 + x2 = -1.449489743 + 1.449489743 Combine like terms: -1.449489743 + 1.449489743 = 0.000000000 1.449489743 + 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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