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Simplifying 20x4 + -110x3 + 12x2 = 0 Reorder the terms: 12x2 + -110x3 + 20x4 = 0 Solving 12x2 + -110x3 + 20x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(6 + -55x + 10x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(6 + -55x + 10x2)' equal to zero and attempt to solve: Simplifying 6 + -55x + 10x2 = 0 Solving 6 + -55x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.6 + -5.5x + x2 = 0.0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -5.5x + -0.6 + x2 = 0.0 + -0.6 Reorder the terms: 0.6 + -0.6 + -5.5x + x2 = 0.0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -5.5x + x2 = 0.0 + -0.6 -5.5x + x2 = 0.0 + -0.6 Combine like terms: 0.0 + -0.6 = -0.6 -5.5x + x2 = -0.6 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -0.6 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -0.6 + 7.5625 Combine like terms: -0.6 + 7.5625 = 6.9625 7.5625 + -5.5x + x2 = 6.9625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 6.9625 Calculate the square root of the right side: 2.63865496 Break this problem into two subproblems by setting (x + -2.75) equal to 2.63865496 and -2.63865496.Subproblem 1
x + -2.75 = 2.63865496 Simplifying x + -2.75 = 2.63865496 Reorder the terms: -2.75 + x = 2.63865496 Solving -2.75 + x = 2.63865496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 2.63865496 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 2.63865496 + 2.75 x = 2.63865496 + 2.75 Combine like terms: 2.63865496 + 2.75 = 5.38865496 x = 5.38865496 Simplifying x = 5.38865496Subproblem 2
x + -2.75 = -2.63865496 Simplifying x + -2.75 = -2.63865496 Reorder the terms: -2.75 + x = -2.63865496 Solving -2.75 + x = -2.63865496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -2.63865496 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -2.63865496 + 2.75 x = -2.63865496 + 2.75 Combine like terms: -2.63865496 + 2.75 = 0.11134504 x = 0.11134504 Simplifying x = 0.11134504Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.38865496, 0.11134504}Solution
x = {0, 5.38865496, 0.11134504}
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