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Simplifying 12x2 + 118x + 6 = 0 Reorder the terms: 6 + 118x + 12x2 = 0 Solving 6 + 118x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 59x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 59x + 6x2)' equal to zero and attempt to solve: Simplifying 3 + 59x + 6x2 = 0 Solving 3 + 59x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.5 + 9.833333333x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 9.833333333x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 9.833333333x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 9.833333333x + x2 = 0 + -0.5 9.833333333x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 9.833333333x + x2 = -0.5 The x term is 9.833333333x. Take half its coefficient (4.916666667). Square it (24.17361111) and add it to both sides. Add '24.17361111' to each side of the equation. 9.833333333x + 24.17361111 + x2 = -0.5 + 24.17361111 Reorder the terms: 24.17361111 + 9.833333333x + x2 = -0.5 + 24.17361111 Combine like terms: -0.5 + 24.17361111 = 23.67361111 24.17361111 + 9.833333333x + x2 = 23.67361111 Factor a perfect square on the left side: (x + 4.916666667)(x + 4.916666667) = 23.67361111 Calculate the square root of the right side: 4.865553526 Break this problem into two subproblems by setting (x + 4.916666667) equal to 4.865553526 and -4.865553526.Subproblem 1
x + 4.916666667 = 4.865553526 Simplifying x + 4.916666667 = 4.865553526 Reorder the terms: 4.916666667 + x = 4.865553526 Solving 4.916666667 + x = 4.865553526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.916666667' to each side of the equation. 4.916666667 + -4.916666667 + x = 4.865553526 + -4.916666667 Combine like terms: 4.916666667 + -4.916666667 = 0.000000000 0.000000000 + x = 4.865553526 + -4.916666667 x = 4.865553526 + -4.916666667 Combine like terms: 4.865553526 + -4.916666667 = -0.051113141 x = -0.051113141 Simplifying x = -0.051113141Subproblem 2
x + 4.916666667 = -4.865553526 Simplifying x + 4.916666667 = -4.865553526 Reorder the terms: 4.916666667 + x = -4.865553526 Solving 4.916666667 + x = -4.865553526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.916666667' to each side of the equation. 4.916666667 + -4.916666667 + x = -4.865553526 + -4.916666667 Combine like terms: 4.916666667 + -4.916666667 = 0.000000000 0.000000000 + x = -4.865553526 + -4.916666667 x = -4.865553526 + -4.916666667 Combine like terms: -4.865553526 + -4.916666667 = -9.782220193 x = -9.782220193 Simplifying x = -9.782220193Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.051113141, -9.782220193}Solution
x = {-0.051113141, -9.782220193}
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