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Simplifying 5x5 + -36x3 + 48x = 0 Reorder the terms: 48x + -36x3 + 5x5 = 0 Solving 48x + -36x3 + 5x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(48 + -36x2 + 5x4) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(48 + -36x2 + 5x4)' equal to zero and attempt to solve: Simplifying 48 + -36x2 + 5x4 = 0 Solving 48 + -36x2 + 5x4 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 9.6 + -7.2x2 + x4 = 0 Move the constant term to the right: Add '-9.6' to each side of the equation. 9.6 + -7.2x2 + -9.6 + x4 = 0 + -9.6 Reorder the terms: 9.6 + -9.6 + -7.2x2 + x4 = 0 + -9.6 Combine like terms: 9.6 + -9.6 = 0.0 0.0 + -7.2x2 + x4 = 0 + -9.6 -7.2x2 + x4 = 0 + -9.6 Combine like terms: 0 + -9.6 = -9.6 -7.2x2 + x4 = -9.6 The x term is -7.2x2. Take half its coefficient (-3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. -7.2x2 + 12.96 + x4 = -9.6 + 12.96 Reorder the terms: 12.96 + -7.2x2 + x4 = -9.6 + 12.96 Combine like terms: -9.6 + 12.96 = 3.36 12.96 + -7.2x2 + x4 = 3.36 Factor a perfect square on the left side: (x2 + -3.6)(x2 + -3.6) = 3.36 Calculate the square root of the right side: 1.833030278 Break this problem into two subproblems by setting (x2 + -3.6) equal to 1.833030278 and -1.833030278.Subproblem 1
x2 + -3.6 = 1.833030278 Simplifying x2 + -3.6 = 1.833030278 Reorder the terms: -3.6 + x2 = 1.833030278 Solving -3.6 + x2 = 1.833030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x2 = 1.833030278 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x2 = 1.833030278 + 3.6 x2 = 1.833030278 + 3.6 Combine like terms: 1.833030278 + 3.6 = 5.433030278 x2 = 5.433030278 Simplifying x2 = 5.433030278 Take the square root of each side: x = {-2.330886157, 2.330886157}Subproblem 2
x2 + -3.6 = -1.833030278 Simplifying x2 + -3.6 = -1.833030278 Reorder the terms: -3.6 + x2 = -1.833030278 Solving -3.6 + x2 = -1.833030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x2 = -1.833030278 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x2 = -1.833030278 + 3.6 x2 = -1.833030278 + 3.6 Combine like terms: -1.833030278 + 3.6 = 1.766969722 x2 = 1.766969722 Simplifying x2 = 1.766969722 Take the square root of each side: x = {-1.329274134, 1.329274134}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.330886157, 2.330886157, -1.329274134, 1.329274134}Solution
x = {0, -2.330886157, 2.330886157, -1.329274134, 1.329274134}
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