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Simplifying 40x4 + -39x2 + -400 = 0 Reorder the terms: -400 + -39x2 + 40x4 = 0 Solving -400 + -39x2 + 40x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -10 + -0.975x2 + x4 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -0.975x2 + 10 + x4 = 0 + 10 Reorder the terms: -10 + 10 + -0.975x2 + x4 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -0.975x2 + x4 = 0 + 10 -0.975x2 + x4 = 0 + 10 Combine like terms: 0 + 10 = 10 -0.975x2 + x4 = 10 The x term is -0.975x2. Take half its coefficient (-0.4875). Square it (0.23765625) and add it to both sides. Add '0.23765625' to each side of the equation. -0.975x2 + 0.23765625 + x4 = 10 + 0.23765625 Reorder the terms: 0.23765625 + -0.975x2 + x4 = 10 + 0.23765625 Combine like terms: 10 + 0.23765625 = 10.23765625 0.23765625 + -0.975x2 + x4 = 10.23765625 Factor a perfect square on the left side: (x2 + -0.4875)(x2 + -0.4875) = 10.23765625 Calculate the square root of the right side: 3.199633768 Break this problem into two subproblems by setting (x2 + -0.4875) equal to 3.199633768 and -3.199633768.Subproblem 1
x2 + -0.4875 = 3.199633768 Simplifying x2 + -0.4875 = 3.199633768 Reorder the terms: -0.4875 + x2 = 3.199633768 Solving -0.4875 + x2 = 3.199633768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4875' to each side of the equation. -0.4875 + 0.4875 + x2 = 3.199633768 + 0.4875 Combine like terms: -0.4875 + 0.4875 = 0.0000 0.0000 + x2 = 3.199633768 + 0.4875 x2 = 3.199633768 + 0.4875 Combine like terms: 3.199633768 + 0.4875 = 3.687133768 x2 = 3.687133768 Simplifying x2 = 3.687133768 Take the square root of each side: x = {-1.920191076, 1.920191076}Subproblem 2
x2 + -0.4875 = -3.199633768 Simplifying x2 + -0.4875 = -3.199633768 Reorder the terms: -0.4875 + x2 = -3.199633768 Solving -0.4875 + x2 = -3.199633768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4875' to each side of the equation. -0.4875 + 0.4875 + x2 = -3.199633768 + 0.4875 Combine like terms: -0.4875 + 0.4875 = 0.0000 0.0000 + x2 = -3.199633768 + 0.4875 x2 = -3.199633768 + 0.4875 Combine like terms: -3.199633768 + 0.4875 = -2.712133768 x2 = -2.712133768 Simplifying x2 = -2.712133768 Reorder the terms: 2.712133768 + x2 = -2.712133768 + 2.712133768 Combine like terms: -2.712133768 + 2.712133768 = 0.000000000 2.712133768 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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