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Simplifying x4 + -30x2 + 115 = 0 Reorder the terms: 115 + -30x2 + x4 = 0 Solving 115 + -30x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-115' to each side of the equation. 115 + -30x2 + -115 + x4 = 0 + -115 Reorder the terms: 115 + -115 + -30x2 + x4 = 0 + -115 Combine like terms: 115 + -115 = 0 0 + -30x2 + x4 = 0 + -115 -30x2 + x4 = 0 + -115 Combine like terms: 0 + -115 = -115 -30x2 + x4 = -115 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 = -115 + 225 Reorder the terms: 225 + -30x2 + x4 = -115 + 225 Combine like terms: -115 + 225 = 110 225 + -30x2 + x4 = 110 Factor a perfect square on the left side: (x2 + -15)(x2 + -15) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (x2 + -15) equal to 10.488088482 and -10.488088482.Subproblem 1
x2 + -15 = 10.488088482 Simplifying x2 + -15 = 10.488088482 Reorder the terms: -15 + x2 = 10.488088482 Solving -15 + x2 = 10.488088482 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 = 10.488088482 + 15 Combine like terms: -15 + 15 = 0 0 + x2 = 10.488088482 + 15 x2 = 10.488088482 + 15 Combine like terms: 10.488088482 + 15 = 25.488088482 x2 = 25.488088482 Simplifying x2 = 25.488088482 Take the square root of each side: x = {-5.048572915, 5.048572915}Subproblem 2
x2 + -15 = -10.488088482 Simplifying x2 + -15 = -10.488088482 Reorder the terms: -15 + x2 = -10.488088482 Solving -15 + x2 = -10.488088482 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 = -10.488088482 + 15 Combine like terms: -15 + 15 = 0 0 + x2 = -10.488088482 + 15 x2 = -10.488088482 + 15 Combine like terms: -10.488088482 + 15 = 4.511911518 x2 = 4.511911518 Simplifying x2 = 4.511911518 Take the square root of each side: x = {-2.12412606, 2.12412606}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.048572915, 5.048572915, -2.12412606, 2.12412606}
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