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Simplifying 0 = x4 + -48x2 + 384 Reorder the terms: 0 = 384 + -48x2 + x4 Solving 0 = 384 + -48x2 + x4 Solving for variable 'x'. Combine like terms: 0 + -384 = -384 -384 + 48x2 + -1x4 = 384 + -48x2 + x4 + -384 + 48x2 + -1x4 Reorder the terms: -384 + 48x2 + -1x4 = 384 + -384 + -48x2 + 48x2 + x4 + -1x4 Combine like terms: 384 + -384 = 0 -384 + 48x2 + -1x4 = 0 + -48x2 + 48x2 + x4 + -1x4 -384 + 48x2 + -1x4 = -48x2 + 48x2 + x4 + -1x4 Combine like terms: -48x2 + 48x2 = 0 -384 + 48x2 + -1x4 = 0 + x4 + -1x4 -384 + 48x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -384 + 48x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 384 + -48x2 + x4 = 0 Move the constant term to the right: Add '-384' to each side of the equation. 384 + -48x2 + -384 + x4 = 0 + -384 Reorder the terms: 384 + -384 + -48x2 + x4 = 0 + -384 Combine like terms: 384 + -384 = 0 0 + -48x2 + x4 = 0 + -384 -48x2 + x4 = 0 + -384 Combine like terms: 0 + -384 = -384 -48x2 + x4 = -384 The x term is -48x2. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48x2 + 576 + x4 = -384 + 576 Reorder the terms: 576 + -48x2 + x4 = -384 + 576 Combine like terms: -384 + 576 = 192 576 + -48x2 + x4 = 192 Factor a perfect square on the left side: (x2 + -24)(x2 + -24) = 192 Calculate the square root of the right side: 13.856406461 Break this problem into two subproblems by setting (x2 + -24) equal to 13.856406461 and -13.856406461.Subproblem 1
x2 + -24 = 13.856406461 Simplifying x2 + -24 = 13.856406461 Reorder the terms: -24 + x2 = 13.856406461 Solving -24 + x2 = 13.856406461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x2 = 13.856406461 + 24 Combine like terms: -24 + 24 = 0 0 + x2 = 13.856406461 + 24 x2 = 13.856406461 + 24 Combine like terms: 13.856406461 + 24 = 37.856406461 x2 = 37.856406461 Simplifying x2 = 37.856406461 Take the square root of each side: x = {-6.152756005, 6.152756005}Subproblem 2
x2 + -24 = -13.856406461 Simplifying x2 + -24 = -13.856406461 Reorder the terms: -24 + x2 = -13.856406461 Solving -24 + x2 = -13.856406461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x2 = -13.856406461 + 24 Combine like terms: -24 + 24 = 0 0 + x2 = -13.856406461 + 24 x2 = -13.856406461 + 24 Combine like terms: -13.856406461 + 24 = 10.143593539 x2 = 10.143593539 Simplifying x2 = 10.143593539 Take the square root of each side: x = {-3.184900868, 3.184900868}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.152756005, 6.152756005, -3.184900868, 3.184900868}
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