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Simplifying 2x4 + -25x2 + 8 = 0 Reorder the terms: 8 + -25x2 + 2x4 = 0 Solving 8 + -25x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + -12.5x2 + x4 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -12.5x2 + -4 + x4 = 0 + -4 Reorder the terms: 4 + -4 + -12.5x2 + x4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -12.5x2 + x4 = 0 + -4 -12.5x2 + x4 = 0 + -4 Combine like terms: 0 + -4 = -4 -12.5x2 + x4 = -4 The x term is -12.5x2. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x2 + 39.0625 + x4 = -4 + 39.0625 Reorder the terms: 39.0625 + -12.5x2 + x4 = -4 + 39.0625 Combine like terms: -4 + 39.0625 = 35.0625 39.0625 + -12.5x2 + x4 = 35.0625 Factor a perfect square on the left side: (x2 + -6.25)(x2 + -6.25) = 35.0625 Calculate the square root of the right side: 5.921359641 Break this problem into two subproblems by setting (x2 + -6.25) equal to 5.921359641 and -5.921359641.Subproblem 1
x2 + -6.25 = 5.921359641 Simplifying x2 + -6.25 = 5.921359641 Reorder the terms: -6.25 + x2 = 5.921359641 Solving -6.25 + x2 = 5.921359641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x2 = 5.921359641 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x2 = 5.921359641 + 6.25 x2 = 5.921359641 + 6.25 Combine like terms: 5.921359641 + 6.25 = 12.171359641 x2 = 12.171359641 Simplifying x2 = 12.171359641 Take the square root of each side: x = {-3.488747575, 3.488747575}Subproblem 2
x2 + -6.25 = -5.921359641 Simplifying x2 + -6.25 = -5.921359641 Reorder the terms: -6.25 + x2 = -5.921359641 Solving -6.25 + x2 = -5.921359641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x2 = -5.921359641 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x2 = -5.921359641 + 6.25 x2 = -5.921359641 + 6.25 Combine like terms: -5.921359641 + 6.25 = 0.328640359 x2 = 0.328640359 Simplifying x2 = 0.328640359 Take the square root of each side: x = {-0.573271628, 0.573271628}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.488747575, 3.488747575, -0.573271628, 0.573271628}
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