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Simplifying x4 + -6.25x2 + 9 = 0 Reorder the terms: 9 + -6.25x2 + x4 = 0 Solving 9 + -6.25x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -6.25x2 + -9 + x4 = 0 + -9 Reorder the terms: 9 + -9 + -6.25x2 + x4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -6.25x2 + x4 = 0 + -9 -6.25x2 + x4 = 0 + -9 Combine like terms: 0 + -9 = -9 -6.25x2 + x4 = -9 The x term is -6.25x2. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x2 + 9.765625 + x4 = -9 + 9.765625 Reorder the terms: 9.765625 + -6.25x2 + x4 = -9 + 9.765625 Combine like terms: -9 + 9.765625 = 0.765625 9.765625 + -6.25x2 + x4 = 0.765625 Factor a perfect square on the left side: (x2 + -3.125)(x2 + -3.125) = 0.765625 Calculate the square root of the right side: 0.875 Break this problem into two subproblems by setting (x2 + -3.125) equal to 0.875 and -0.875.Subproblem 1
x2 + -3.125 = 0.875 Simplifying x2 + -3.125 = 0.875 Reorder the terms: -3.125 + x2 = 0.875 Solving -3.125 + x2 = 0.875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x2 = 0.875 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x2 = 0.875 + 3.125 x2 = 0.875 + 3.125 Combine like terms: 0.875 + 3.125 = 4 x2 = 4 Simplifying x2 = 4 Take the square root of each side: x = {-2, 2}Subproblem 2
x2 + -3.125 = -0.875 Simplifying x2 + -3.125 = -0.875 Reorder the terms: -3.125 + x2 = -0.875 Solving -3.125 + x2 = -0.875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x2 = -0.875 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x2 = -0.875 + 3.125 x2 = -0.875 + 3.125 Combine like terms: -0.875 + 3.125 = 2.25 x2 = 2.25 Simplifying x2 = 2.25 Take the square root of each side: x = {-1.5, 1.5}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2, 2, -1.5, 1.5}
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