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Simplifying x4 + -16.25x2 = -4 Reorder the terms: -16.25x2 + x4 = -4 Solving -16.25x2 + x4 = -4 Solving for variable 'x'. Reorder the terms: 4 + -16.25x2 + x4 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + -16.25x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -16.25x2 + -4 + x4 = 0 + -4 Reorder the terms: 4 + -4 + -16.25x2 + x4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -16.25x2 + x4 = 0 + -4 -16.25x2 + x4 = 0 + -4 Combine like terms: 0 + -4 = -4 -16.25x2 + x4 = -4 The x term is -16.25x2. Take half its coefficient (-8.125). Square it (66.015625) and add it to both sides. Add '66.015625' to each side of the equation. -16.25x2 + 66.015625 + x4 = -4 + 66.015625 Reorder the terms: 66.015625 + -16.25x2 + x4 = -4 + 66.015625 Combine like terms: -4 + 66.015625 = 62.015625 66.015625 + -16.25x2 + x4 = 62.015625 Factor a perfect square on the left side: (x2 + -8.125)(x2 + -8.125) = 62.015625 Calculate the square root of the right side: 7.875 Break this problem into two subproblems by setting (x2 + -8.125) equal to 7.875 and -7.875.Subproblem 1
x2 + -8.125 = 7.875 Simplifying x2 + -8.125 = 7.875 Reorder the terms: -8.125 + x2 = 7.875 Solving -8.125 + x2 = 7.875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.125' to each side of the equation. -8.125 + 8.125 + x2 = 7.875 + 8.125 Combine like terms: -8.125 + 8.125 = 0.000 0.000 + x2 = 7.875 + 8.125 x2 = 7.875 + 8.125 Combine like terms: 7.875 + 8.125 = 16 x2 = 16 Simplifying x2 = 16 Take the square root of each side: x = {-4, 4}Subproblem 2
x2 + -8.125 = -7.875 Simplifying x2 + -8.125 = -7.875 Reorder the terms: -8.125 + x2 = -7.875 Solving -8.125 + x2 = -7.875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.125' to each side of the equation. -8.125 + 8.125 + x2 = -7.875 + 8.125 Combine like terms: -8.125 + 8.125 = 0.000 0.000 + x2 = -7.875 + 8.125 x2 = -7.875 + 8.125 Combine like terms: -7.875 + 8.125 = 0.25 x2 = 0.25 Simplifying x2 = 0.25 Take the square root of each side: x = {-0.5, 0.5}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4, 4, -0.5, 0.5}
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