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Simplifying x4 + -26x2 + 15 = 0 Reorder the terms: 15 + -26x2 + x4 = 0 Solving 15 + -26x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -26x2 + -15 + x4 = 0 + -15 Reorder the terms: 15 + -15 + -26x2 + x4 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -26x2 + x4 = 0 + -15 -26x2 + x4 = 0 + -15 Combine like terms: 0 + -15 = -15 -26x2 + x4 = -15 The x term is -26x2. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x2 + 169 + x4 = -15 + 169 Reorder the terms: 169 + -26x2 + x4 = -15 + 169 Combine like terms: -15 + 169 = 154 169 + -26x2 + x4 = 154 Factor a perfect square on the left side: (x2 + -13)(x2 + -13) = 154 Calculate the square root of the right side: 12.409673646 Break this problem into two subproblems by setting (x2 + -13) equal to 12.409673646 and -12.409673646.Subproblem 1
x2 + -13 = 12.409673646 Simplifying x2 + -13 = 12.409673646 Reorder the terms: -13 + x2 = 12.409673646 Solving -13 + x2 = 12.409673646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x2 = 12.409673646 + 13 Combine like terms: -13 + 13 = 0 0 + x2 = 12.409673646 + 13 x2 = 12.409673646 + 13 Combine like terms: 12.409673646 + 13 = 25.409673646 x2 = 25.409673646 Simplifying x2 = 25.409673646 Take the square root of each side: x = {-5.040800893, 5.040800893}Subproblem 2
x2 + -13 = -12.409673646 Simplifying x2 + -13 = -12.409673646 Reorder the terms: -13 + x2 = -12.409673646 Solving -13 + x2 = -12.409673646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x2 = -12.409673646 + 13 Combine like terms: -13 + 13 = 0 0 + x2 = -12.409673646 + 13 x2 = -12.409673646 + 13 Combine like terms: -12.409673646 + 13 = 0.590326354 x2 = 0.590326354 Simplifying x2 = 0.590326354 Take the square root of each side: x = {-0.768326984, 0.768326984}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.040800893, 5.040800893, -0.768326984, 0.768326984}
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