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Simplifying 6x2 + 76x + -22 = 0 Reorder the terms: -22 + 76x + 6x2 = 0 Solving -22 + 76x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + 38x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + 38x + 3x2)' equal to zero and attempt to solve: Simplifying -11 + 38x + 3x2 = 0 Solving -11 + 38x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.666666667 + 12.66666667x + x2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + 12.66666667x + 3.666666667 + x2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + 12.66666667x + x2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + 12.66666667x + x2 = 0 + 3.666666667 12.66666667x + x2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 12.66666667x + x2 = 3.666666667 The x term is 12.66666667x. Take half its coefficient (6.333333335). Square it (40.11111113) and add it to both sides. Add '40.11111113' to each side of the equation. 12.66666667x + 40.11111113 + x2 = 3.666666667 + 40.11111113 Reorder the terms: 40.11111113 + 12.66666667x + x2 = 3.666666667 + 40.11111113 Combine like terms: 3.666666667 + 40.11111113 = 43.777777797 40.11111113 + 12.66666667x + x2 = 43.777777797 Factor a perfect square on the left side: (x + 6.333333335)(x + 6.333333335) = 43.777777797 Calculate the square root of the right side: 6.616477749 Break this problem into two subproblems by setting (x + 6.333333335) equal to 6.616477749 and -6.616477749.Subproblem 1
x + 6.333333335 = 6.616477749 Simplifying x + 6.333333335 = 6.616477749 Reorder the terms: 6.333333335 + x = 6.616477749 Solving 6.333333335 + x = 6.616477749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.333333335' to each side of the equation. 6.333333335 + -6.333333335 + x = 6.616477749 + -6.333333335 Combine like terms: 6.333333335 + -6.333333335 = 0.000000000 0.000000000 + x = 6.616477749 + -6.333333335 x = 6.616477749 + -6.333333335 Combine like terms: 6.616477749 + -6.333333335 = 0.283144414 x = 0.283144414 Simplifying x = 0.283144414Subproblem 2
x + 6.333333335 = -6.616477749 Simplifying x + 6.333333335 = -6.616477749 Reorder the terms: 6.333333335 + x = -6.616477749 Solving 6.333333335 + x = -6.616477749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.333333335' to each side of the equation. 6.333333335 + -6.333333335 + x = -6.616477749 + -6.333333335 Combine like terms: 6.333333335 + -6.333333335 = 0.000000000 0.000000000 + x = -6.616477749 + -6.333333335 x = -6.616477749 + -6.333333335 Combine like terms: -6.616477749 + -6.333333335 = -12.949811084 x = -12.949811084 Simplifying x = -12.949811084Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.283144414, -12.949811084}Solution
x = {0.283144414, -12.949811084}
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