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Simplifying x4 + -28x2 + 100 = 0 Reorder the terms: 100 + -28x2 + x4 = 0 Solving 100 + -28x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -28x2 + -100 + x4 = 0 + -100 Reorder the terms: 100 + -100 + -28x2 + x4 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -28x2 + x4 = 0 + -100 -28x2 + x4 = 0 + -100 Combine like terms: 0 + -100 = -100 -28x2 + x4 = -100 The x term is -28x2. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x2 + 196 + x4 = -100 + 196 Reorder the terms: 196 + -28x2 + x4 = -100 + 196 Combine like terms: -100 + 196 = 96 196 + -28x2 + x4 = 96 Factor a perfect square on the left side: (x2 + -14)(x2 + -14) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x2 + -14) equal to 9.797958971 and -9.797958971.Subproblem 1
x2 + -14 = 9.797958971 Simplifying x2 + -14 = 9.797958971 Reorder the terms: -14 + x2 = 9.797958971 Solving -14 + x2 = 9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x2 = 9.797958971 + 14 Combine like terms: -14 + 14 = 0 0 + x2 = 9.797958971 + 14 x2 = 9.797958971 + 14 Combine like terms: 9.797958971 + 14 = 23.797958971 x2 = 23.797958971 Simplifying x2 = 23.797958971 Take the square root of each side: x = {-4.878315177, 4.878315177}Subproblem 2
x2 + -14 = -9.797958971 Simplifying x2 + -14 = -9.797958971 Reorder the terms: -14 + x2 = -9.797958971 Solving -14 + x2 = -9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x2 = -9.797958971 + 14 Combine like terms: -14 + 14 = 0 0 + x2 = -9.797958971 + 14 x2 = -9.797958971 + 14 Combine like terms: -9.797958971 + 14 = 4.202041029 x2 = 4.202041029 Simplifying x2 = 4.202041029 Take the square root of each side: x = {-2.049888053, 2.049888053}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.878315177, 4.878315177, -2.049888053, 2.049888053}
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