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Simplifying 20x4 + -138x2 + 120 = 0 Reorder the terms: 120 + -138x2 + 20x4 = 0 Solving 120 + -138x2 + 20x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(60 + -69x2 + 10x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(60 + -69x2 + 10x4)' equal to zero and attempt to solve: Simplifying 60 + -69x2 + 10x4 = 0 Solving 60 + -69x2 + 10x4 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 6 + -6.9x2 + x4 = 0.0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -6.9x2 + -6 + x4 = 0.0 + -6 Reorder the terms: 6 + -6 + -6.9x2 + x4 = 0.0 + -6 Combine like terms: 6 + -6 = 0 0 + -6.9x2 + x4 = 0.0 + -6 -6.9x2 + x4 = 0.0 + -6 Combine like terms: 0.0 + -6 = -6 -6.9x2 + x4 = -6 The x term is -6.9x2. Take half its coefficient (-3.45). Square it (11.9025) and add it to both sides. Add '11.9025' to each side of the equation. -6.9x2 + 11.9025 + x4 = -6 + 11.9025 Reorder the terms: 11.9025 + -6.9x2 + x4 = -6 + 11.9025 Combine like terms: -6 + 11.9025 = 5.9025 11.9025 + -6.9x2 + x4 = 5.9025 Factor a perfect square on the left side: (x2 + -3.45)(x2 + -3.45) = 5.9025 Calculate the square root of the right side: 2.429506123 Break this problem into two subproblems by setting (x2 + -3.45) equal to 2.429506123 and -2.429506123.Subproblem 1
x2 + -3.45 = 2.429506123 Simplifying x2 + -3.45 = 2.429506123 Reorder the terms: -3.45 + x2 = 2.429506123 Solving -3.45 + x2 = 2.429506123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.45' to each side of the equation. -3.45 + 3.45 + x2 = 2.429506123 + 3.45 Combine like terms: -3.45 + 3.45 = 0.00 0.00 + x2 = 2.429506123 + 3.45 x2 = 2.429506123 + 3.45 Combine like terms: 2.429506123 + 3.45 = 5.879506123 x2 = 5.879506123 Simplifying x2 = 5.879506123 Take the square root of each side: x = {-2.424769293, 2.424769293}Subproblem 2
x2 + -3.45 = -2.429506123 Simplifying x2 + -3.45 = -2.429506123 Reorder the terms: -3.45 + x2 = -2.429506123 Solving -3.45 + x2 = -2.429506123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.45' to each side of the equation. -3.45 + 3.45 + x2 = -2.429506123 + 3.45 Combine like terms: -3.45 + 3.45 = 0.00 0.00 + x2 = -2.429506123 + 3.45 x2 = -2.429506123 + 3.45 Combine like terms: -2.429506123 + 3.45 = 1.020493877 x2 = 1.020493877 Simplifying x2 = 1.020493877 Take the square root of each side: x = {-1.01019497, 1.01019497}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.424769293, 2.424769293, -1.01019497, 1.01019497}Solution
x = {-2.424769293, 2.424769293, -1.01019497, 1.01019497}
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