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Simplifying x4 + -30x2 + 124 = 0 Reorder the terms: 124 + -30x2 + x4 = 0 Solving 124 + -30x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-124' to each side of the equation. 124 + -30x2 + -124 + x4 = 0 + -124 Reorder the terms: 124 + -124 + -30x2 + x4 = 0 + -124 Combine like terms: 124 + -124 = 0 0 + -30x2 + x4 = 0 + -124 -30x2 + x4 = 0 + -124 Combine like terms: 0 + -124 = -124 -30x2 + x4 = -124 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 = -124 + 225 Reorder the terms: 225 + -30x2 + x4 = -124 + 225 Combine like terms: -124 + 225 = 101 225 + -30x2 + x4 = 101 Factor a perfect square on the left side: (x2 + -15)(x2 + -15) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (x2 + -15) equal to 10.049875621 and -10.049875621.Subproblem 1
x2 + -15 = 10.049875621 Simplifying x2 + -15 = 10.049875621 Reorder the terms: -15 + x2 = 10.049875621 Solving -15 + x2 = 10.049875621 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 = 10.049875621 + 15 Combine like terms: -15 + 15 = 0 0 + x2 = 10.049875621 + 15 x2 = 10.049875621 + 15 Combine like terms: 10.049875621 + 15 = 25.049875621 x2 = 25.049875621 Simplifying x2 = 25.049875621 Take the square root of each side: x = {-5.004985077, 5.004985077}Subproblem 2
x2 + -15 = -10.049875621 Simplifying x2 + -15 = -10.049875621 Reorder the terms: -15 + x2 = -10.049875621 Solving -15 + x2 = -10.049875621 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 = -10.049875621 + 15 Combine like terms: -15 + 15 = 0 0 + x2 = -10.049875621 + 15 x2 = -10.049875621 + 15 Combine like terms: -10.049875621 + 15 = 4.950124379 x2 = 4.950124379 Simplifying x2 = 4.950124379 Take the square root of each side: x = {-2.224887498, 2.224887498}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.004985077, 5.004985077, -2.224887498, 2.224887498}
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