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Simplifying 6x2 + 64x + -12 = 0 Reorder the terms: -12 + 64x + 6x2 = 0 Solving -12 + 64x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 32x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 32x + 3x2)' equal to zero and attempt to solve: Simplifying -6 + 32x + 3x2 = 0 Solving -6 + 32x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + 10.66666667x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 10.66666667x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 10.66666667x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 10.66666667x + x2 = 0 + 2 10.66666667x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 10.66666667x + x2 = 2 The x term is 10.66666667x. Take half its coefficient (5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. 10.66666667x + 28.44444446 + x2 = 2 + 28.44444446 Reorder the terms: 28.44444446 + 10.66666667x + x2 = 2 + 28.44444446 Combine like terms: 2 + 28.44444446 = 30.44444446 28.44444446 + 10.66666667x + x2 = 30.44444446 Factor a perfect square on the left side: (x + 5.333333335)(x + 5.333333335) = 30.44444446 Calculate the square root of the right side: 5.517648454 Break this problem into two subproblems by setting (x + 5.333333335) equal to 5.517648454 and -5.517648454.Subproblem 1
x + 5.333333335 = 5.517648454 Simplifying x + 5.333333335 = 5.517648454 Reorder the terms: 5.333333335 + x = 5.517648454 Solving 5.333333335 + x = 5.517648454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = 5.517648454 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = 5.517648454 + -5.333333335 x = 5.517648454 + -5.333333335 Combine like terms: 5.517648454 + -5.333333335 = 0.184315119 x = 0.184315119 Simplifying x = 0.184315119Subproblem 2
x + 5.333333335 = -5.517648454 Simplifying x + 5.333333335 = -5.517648454 Reorder the terms: 5.333333335 + x = -5.517648454 Solving 5.333333335 + x = -5.517648454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = -5.517648454 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = -5.517648454 + -5.333333335 x = -5.517648454 + -5.333333335 Combine like terms: -5.517648454 + -5.333333335 = -10.850981789 x = -10.850981789 Simplifying x = -10.850981789Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.184315119, -10.850981789}Solution
x = {0.184315119, -10.850981789}
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