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Simplifying 20x2 + 120x + 62 = 0 Reorder the terms: 62 + 120x + 20x2 = 0 Solving 62 + 120x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(31 + 60x + 10x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(31 + 60x + 10x2)' equal to zero and attempt to solve: Simplifying 31 + 60x + 10x2 = 0 Solving 31 + 60x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 3.1 + 6x + x2 = 0.0 Move the constant term to the right: Add '-3.1' to each side of the equation. 3.1 + 6x + -3.1 + x2 = 0.0 + -3.1 Reorder the terms: 3.1 + -3.1 + 6x + x2 = 0.0 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + 6x + x2 = 0.0 + -3.1 6x + x2 = 0.0 + -3.1 Combine like terms: 0.0 + -3.1 = -3.1 6x + x2 = -3.1 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 = -3.1 + 9 Reorder the terms: 9 + 6x + x2 = -3.1 + 9 Combine like terms: -3.1 + 9 = 5.9 9 + 6x + x2 = 5.9 Factor a perfect square on the left side: (x + 3)(x + 3) = 5.9 Calculate the square root of the right side: 2.42899156 Break this problem into two subproblems by setting (x + 3) equal to 2.42899156 and -2.42899156.Subproblem 1
x + 3 = 2.42899156 Simplifying x + 3 = 2.42899156 Reorder the terms: 3 + x = 2.42899156 Solving 3 + x = 2.42899156 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 = 2.42899156 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.42899156 + -3 x = 2.42899156 + -3 Combine like terms: 2.42899156 + -3 = -0.57100844 x = -0.57100844 Simplifying x = -0.57100844Subproblem 2
x + 3 = -2.42899156 Simplifying x + 3 = -2.42899156 Reorder the terms: 3 + x = -2.42899156 Solving 3 + x = -2.42899156 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 = -2.42899156 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.42899156 + -3 x = -2.42899156 + -3 Combine like terms: -2.42899156 + -3 = -5.42899156 x = -5.42899156 Simplifying x = -5.42899156Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.57100844, -5.42899156}Solution
x = {-0.57100844, -5.42899156}
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