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Simplifying 20x2 + 120x + 24 = 0 Reorder the terms: 24 + 120x + 20x2 = 0 Solving 24 + 120x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(6 + 30x + 5x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(6 + 30x + 5x2)' equal to zero and attempt to solve: Simplifying 6 + 30x + 5x2 = 0 Solving 6 + 30x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + 6x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + 6x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + 6x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + 6x + x2 = 0 + -1.2 6x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 6x + x2 = -1.2 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -1.2 + 9 Reorder the terms: 9 + 6x + x2 = -1.2 + 9 Combine like terms: -1.2 + 9 = 7.8 9 + 6x + x2 = 7.8 Factor a perfect square on the left side: (x + 3)(x + 3) = 7.8 Calculate the square root of the right side: 2.792848009 Break this problem into two subproblems by setting (x + 3) equal to 2.792848009 and -2.792848009.Subproblem 1
x + 3 = 2.792848009 Simplifying x + 3 = 2.792848009 Reorder the terms: 3 + x = 2.792848009 Solving 3 + x = 2.792848009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 2.792848009 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.792848009 + -3 x = 2.792848009 + -3 Combine like terms: 2.792848009 + -3 = -0.207151991 x = -0.207151991 Simplifying x = -0.207151991Subproblem 2
x + 3 = -2.792848009 Simplifying x + 3 = -2.792848009 Reorder the terms: 3 + x = -2.792848009 Solving 3 + x = -2.792848009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -2.792848009 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.792848009 + -3 x = -2.792848009 + -3 Combine like terms: -2.792848009 + -3 = -5.792848009 x = -5.792848009 Simplifying x = -5.792848009Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.207151991, -5.792848009}Solution
x = {-0.207151991, -5.792848009}
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