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Simplifying x4 + -12x2 = -26 Reorder the terms: -12x2 + x4 = -26 Solving -12x2 + x4 = -26 Solving for variable 'x'. Reorder the terms: 26 + -12x2 + x4 = -26 + 26 Combine like terms: -26 + 26 = 0 26 + -12x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + -12x2 + -26 + x4 = 0 + -26 Reorder the terms: 26 + -26 + -12x2 + x4 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -12x2 + x4 = 0 + -26 -12x2 + x4 = 0 + -26 Combine like terms: 0 + -26 = -26 -12x2 + x4 = -26 The x term is -12x2. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x2 + 36 + x4 = -26 + 36 Reorder the terms: 36 + -12x2 + x4 = -26 + 36 Combine like terms: -26 + 36 = 10 36 + -12x2 + x4 = 10 Factor a perfect square on the left side: (x2 + -6)(x2 + -6) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x2 + -6) equal to 3.16227766 and -3.16227766.Subproblem 1
x2 + -6 = 3.16227766 Simplifying x2 + -6 = 3.16227766 Reorder the terms: -6 + x2 = 3.16227766 Solving -6 + x2 = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x2 = 3.16227766 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = 3.16227766 + 6 x2 = 3.16227766 + 6 Combine like terms: 3.16227766 + 6 = 9.16227766 x2 = 9.16227766 Simplifying x2 = 9.16227766 Take the square root of each side: x = {-3.026925447, 3.026925447}Subproblem 2
x2 + -6 = -3.16227766 Simplifying x2 + -6 = -3.16227766 Reorder the terms: -6 + x2 = -3.16227766 Solving -6 + x2 = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x2 = -3.16227766 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = -3.16227766 + 6 x2 = -3.16227766 + 6 Combine like terms: -3.16227766 + 6 = 2.83772234 x2 = 2.83772234 Simplifying x2 = 2.83772234 Take the square root of each side: x = {-1.684554048, 1.684554048}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.026925447, 3.026925447, -1.684554048, 1.684554048}
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