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Simplifying 6x4 + -30x2 + 20 = 0 Reorder the terms: 20 + -30x2 + 6x4 = 0 Solving 20 + -30x2 + 6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -15x2 + 3x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + -15x2 + 3x4)' equal to zero and attempt to solve: Simplifying 10 + -15x2 + 3x4 = 0 Solving 10 + -15x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.333333333 + -5x2 + x4 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + -5x2 + -3.333333333 + x4 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + -5x2 + x4 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + -5x2 + x4 = 0 + -3.333333333 -5x2 + x4 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 -5x2 + x4 = -3.333333333 The x term is -5x2. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x2 + 6.25 + x4 = -3.333333333 + 6.25 Reorder the terms: 6.25 + -5x2 + x4 = -3.333333333 + 6.25 Combine like terms: -3.333333333 + 6.25 = 2.916666667 6.25 + -5x2 + x4 = 2.916666667 Factor a perfect square on the left side: (x2 + -2.5)(x2 + -2.5) = 2.916666667 Calculate the square root of the right side: 1.707825128 Break this problem into two subproblems by setting (x2 + -2.5) equal to 1.707825128 and -1.707825128.Subproblem 1
x2 + -2.5 = 1.707825128 Simplifying x2 + -2.5 = 1.707825128 Reorder the terms: -2.5 + x2 = 1.707825128 Solving -2.5 + x2 = 1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = 1.707825128 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = 1.707825128 + 2.5 x2 = 1.707825128 + 2.5 Combine like terms: 1.707825128 + 2.5 = 4.207825128 x2 = 4.207825128 Simplifying x2 = 4.207825128 Take the square root of each side: x = {-2.051298401, 2.051298401}Subproblem 2
x2 + -2.5 = -1.707825128 Simplifying x2 + -2.5 = -1.707825128 Reorder the terms: -2.5 + x2 = -1.707825128 Solving -2.5 + x2 = -1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = -1.707825128 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = -1.707825128 + 2.5 x2 = -1.707825128 + 2.5 Combine like terms: -1.707825128 + 2.5 = 0.792174872 x2 = 0.792174872 Simplifying x2 = 0.792174872 Take the square root of each side: x = {-0.890042062, 0.890042062}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.051298401, 2.051298401, -0.890042062, 0.890042062}Solution
x = {-2.051298401, 2.051298401, -0.890042062, 0.890042062}
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