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Simplifying 60x4 + -180x2 + 48 = 0 Reorder the terms: 48 + -180x2 + 60x4 = 0 Solving 48 + -180x2 + 60x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(4 + -15x2 + 5x4) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(4 + -15x2 + 5x4)' equal to zero and attempt to solve: Simplifying 4 + -15x2 + 5x4 = 0 Solving 4 + -15x2 + 5x4 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -3x2 + x4 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -3x2 + -0.8 + x4 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -3x2 + x4 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -3x2 + x4 = 0 + -0.8 -3x2 + x4 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -3x2 + x4 = -0.8 The x term is -3x2. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x2 + 2.25 + x4 = -0.8 + 2.25 Reorder the terms: 2.25 + -3x2 + x4 = -0.8 + 2.25 Combine like terms: -0.8 + 2.25 = 1.45 2.25 + -3x2 + x4 = 1.45 Factor a perfect square on the left side: (x2 + -1.5)(x2 + -1.5) = 1.45 Calculate the square root of the right side: 1.204159458 Break this problem into two subproblems by setting (x2 + -1.5) equal to 1.204159458 and -1.204159458.Subproblem 1
x2 + -1.5 = 1.204159458 Simplifying x2 + -1.5 = 1.204159458 Reorder the terms: -1.5 + x2 = 1.204159458 Solving -1.5 + x2 = 1.204159458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = 1.204159458 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = 1.204159458 + 1.5 x2 = 1.204159458 + 1.5 Combine like terms: 1.204159458 + 1.5 = 2.704159458 x2 = 2.704159458 Simplifying x2 = 2.704159458 Take the square root of each side: x = {-1.644432868, 1.644432868}Subproblem 2
x2 + -1.5 = -1.204159458 Simplifying x2 + -1.5 = -1.204159458 Reorder the terms: -1.5 + x2 = -1.204159458 Solving -1.5 + x2 = -1.204159458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = -1.204159458 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = -1.204159458 + 1.5 x2 = -1.204159458 + 1.5 Combine like terms: -1.204159458 + 1.5 = 0.295840542 x2 = 0.295840542 Simplifying x2 = 0.295840542 Take the square root of each side: x = {-0.543912256, 0.543912256}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.644432868, 1.644432868, -0.543912256, 0.543912256}Solution
x = {-1.644432868, 1.644432868, -0.543912256, 0.543912256}
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