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Simplifying x4 + -30x2 + 135 = 0 Reorder the terms: 135 + -30x2 + x4 = 0 Solving 135 + -30x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-135' to each side of the equation. 135 + -30x2 + -135 + x4 = 0 + -135 Reorder the terms: 135 + -135 + -30x2 + x4 = 0 + -135 Combine like terms: 135 + -135 = 0 0 + -30x2 + x4 = 0 + -135 -30x2 + x4 = 0 + -135 Combine like terms: 0 + -135 = -135 -30x2 + x4 = -135 The x term is -30x2. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x2 + 225 + x4 = -135 + 225 Reorder the terms: 225 + -30x2 + x4 = -135 + 225 Combine like terms: -135 + 225 = 90 225 + -30x2 + x4 = 90 Factor a perfect square on the left side: (x2 + -15)(x2 + -15) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (x2 + -15) equal to 9.486832981 and -9.486832981.Subproblem 1
x2 + -15 = 9.486832981 Simplifying x2 + -15 = 9.486832981 Reorder the terms: -15 + x2 = 9.486832981 Solving -15 + x2 = 9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x2 = 9.486832981 + 15 Combine like terms: -15 + 15 = 0 0 + x2 = 9.486832981 + 15 x2 = 9.486832981 + 15 Combine like terms: 9.486832981 + 15 = 24.486832981 x2 = 24.486832981 Simplifying x2 = 24.486832981 Take the square root of each side: x = {-4.94841722, 4.94841722}Subproblem 2
x2 + -15 = -9.486832981 Simplifying x2 + -15 = -9.486832981 Reorder the terms: -15 + x2 = -9.486832981 Solving -15 + x2 = -9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x2 = -9.486832981 + 15 Combine like terms: -15 + 15 = 0 0 + x2 = -9.486832981 + 15 x2 = -9.486832981 + 15 Combine like terms: -9.486832981 + 15 = 5.513167019 x2 = 5.513167019 Simplifying x2 = 5.513167019 Take the square root of each side: x = {-2.34801342, 2.34801342}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.94841722, 4.94841722, -2.34801342, 2.34801342}
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