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Simplifying 20x4 + -145x2 + 252 = 0 Reorder the terms: 252 + -145x2 + 20x4 = 0 Solving 252 + -145x2 + 20x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 12.6 + -7.25x2 + x4 = 0 Move the constant term to the right: Add '-12.6' to each side of the equation. 12.6 + -7.25x2 + -12.6 + x4 = 0 + -12.6 Reorder the terms: 12.6 + -12.6 + -7.25x2 + x4 = 0 + -12.6 Combine like terms: 12.6 + -12.6 = 0.0 0.0 + -7.25x2 + x4 = 0 + -12.6 -7.25x2 + x4 = 0 + -12.6 Combine like terms: 0 + -12.6 = -12.6 -7.25x2 + x4 = -12.6 The x term is -7.25x2. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25x2 + 13.140625 + x4 = -12.6 + 13.140625 Reorder the terms: 13.140625 + -7.25x2 + x4 = -12.6 + 13.140625 Combine like terms: -12.6 + 13.140625 = 0.540625 13.140625 + -7.25x2 + x4 = 0.540625 Factor a perfect square on the left side: (x2 + -3.625)(x2 + -3.625) = 0.540625 Calculate the square root of the right side: 0.735272058 Break this problem into two subproblems by setting (x2 + -3.625) equal to 0.735272058 and -0.735272058.Subproblem 1
x2 + -3.625 = 0.735272058 Simplifying x2 + -3.625 = 0.735272058 Reorder the terms: -3.625 + x2 = 0.735272058 Solving -3.625 + x2 = 0.735272058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x2 = 0.735272058 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x2 = 0.735272058 + 3.625 x2 = 0.735272058 + 3.625 Combine like terms: 0.735272058 + 3.625 = 4.360272058 x2 = 4.360272058 Simplifying x2 = 4.360272058 Take the square root of each side: x = {-2.088126447, 2.088126447}Subproblem 2
x2 + -3.625 = -0.735272058 Simplifying x2 + -3.625 = -0.735272058 Reorder the terms: -3.625 + x2 = -0.735272058 Solving -3.625 + x2 = -0.735272058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x2 = -0.735272058 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x2 = -0.735272058 + 3.625 x2 = -0.735272058 + 3.625 Combine like terms: -0.735272058 + 3.625 = 2.889727942 x2 = 2.889727942 Simplifying x2 = 2.889727942 Take the square root of each side: x = {-1.699919981, 1.699919981}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.088126447, 2.088126447, -1.699919981, 1.699919981}
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