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Simplifying -12x2 + -119x + -5 = 0 Reorder the terms: -5 + -119x + -12x2 = 0 Solving -5 + -119x + -12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 119x + 12x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 119x + 12x2)' equal to zero and attempt to solve: Simplifying 5 + 119x + 12x2 = 0 Solving 5 + 119x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.4166666667 + 9.916666667x + x2 = 0 Move the constant term to the right: Add '-0.4166666667' to each side of the equation. 0.4166666667 + 9.916666667x + -0.4166666667 + x2 = 0 + -0.4166666667 Reorder the terms: 0.4166666667 + -0.4166666667 + 9.916666667x + x2 = 0 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + 9.916666667x + x2 = 0 + -0.4166666667 9.916666667x + x2 = 0 + -0.4166666667 Combine like terms: 0 + -0.4166666667 = -0.4166666667 9.916666667x + x2 = -0.4166666667 The x term is 9.916666667x. Take half its coefficient (4.958333334). Square it (24.58506945) and add it to both sides. Add '24.58506945' to each side of the equation. 9.916666667x + 24.58506945 + x2 = -0.4166666667 + 24.58506945 Reorder the terms: 24.58506945 + 9.916666667x + x2 = -0.4166666667 + 24.58506945 Combine like terms: -0.4166666667 + 24.58506945 = 24.1684027833 24.58506945 + 9.916666667x + x2 = 24.1684027833 Factor a perfect square on the left side: (x + 4.958333334)(x + 4.958333334) = 24.1684027833 Calculate the square root of the right side: 4.916136978 Break this problem into two subproblems by setting (x + 4.958333334) equal to 4.916136978 and -4.916136978.Subproblem 1
x + 4.958333334 = 4.916136978 Simplifying x + 4.958333334 = 4.916136978 Reorder the terms: 4.958333334 + x = 4.916136978 Solving 4.958333334 + x = 4.916136978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.958333334' to each side of the equation. 4.958333334 + -4.958333334 + x = 4.916136978 + -4.958333334 Combine like terms: 4.958333334 + -4.958333334 = 0.000000000 0.000000000 + x = 4.916136978 + -4.958333334 x = 4.916136978 + -4.958333334 Combine like terms: 4.916136978 + -4.958333334 = -0.042196356 x = -0.042196356 Simplifying x = -0.042196356Subproblem 2
x + 4.958333334 = -4.916136978 Simplifying x + 4.958333334 = -4.916136978 Reorder the terms: 4.958333334 + x = -4.916136978 Solving 4.958333334 + x = -4.916136978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.958333334' to each side of the equation. 4.958333334 + -4.958333334 + x = -4.916136978 + -4.958333334 Combine like terms: 4.958333334 + -4.958333334 = 0.000000000 0.000000000 + x = -4.916136978 + -4.958333334 x = -4.916136978 + -4.958333334 Combine like terms: -4.916136978 + -4.958333334 = -9.874470312 x = -9.874470312 Simplifying x = -9.874470312Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.042196356, -9.874470312}Solution
x = {-0.042196356, -9.874470312}
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