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Simplifying 120 = 2x2 + 12x Reorder the terms: 120 = 12x + 2x2 Solving 120 = 12x + 2x2 Solving for variable 'x'. Reorder the terms: 120 + -12x + -2x2 = 12x + -12x + 2x2 + -2x2 Combine like terms: 12x + -12x = 0 120 + -12x + -2x2 = 0 + 2x2 + -2x2 120 + -12x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 120 + -12x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(60 + -6x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(60 + -6x + -1x2)' equal to zero and attempt to solve: Simplifying 60 + -6x + -1x2 = 0 Solving 60 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -60 + 6x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 6x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 6x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 6x + x2 = 0 + 60 6x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 6x + x2 = 60 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 = 60 + 9 Reorder the terms: 9 + 6x + x2 = 60 + 9 Combine like terms: 60 + 9 = 69 9 + 6x + x2 = 69 Factor a perfect square on the left side: (x + 3)(x + 3) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (x + 3) equal to 8.306623863 and -8.306623863.Subproblem 1
x + 3 = 8.306623863 Simplifying x + 3 = 8.306623863 Reorder the terms: 3 + x = 8.306623863 Solving 3 + x = 8.306623863 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 = 8.306623863 + -3 Combine like terms: 3 + -3 = 0 0 + x = 8.306623863 + -3 x = 8.306623863 + -3 Combine like terms: 8.306623863 + -3 = 5.306623863 x = 5.306623863 Simplifying x = 5.306623863Subproblem 2
x + 3 = -8.306623863 Simplifying x + 3 = -8.306623863 Reorder the terms: 3 + x = -8.306623863 Solving 3 + x = -8.306623863 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 = -8.306623863 + -3 Combine like terms: 3 + -3 = 0 0 + x = -8.306623863 + -3 x = -8.306623863 + -3 Combine like terms: -8.306623863 + -3 = -11.306623863 x = -11.306623863 Simplifying x = -11.306623863Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.306623863, -11.306623863}Solution
x = {5.306623863, -11.306623863}
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