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Simplifying 180 + -76x + 6x2 = 0 Solving 180 + -76x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(90 + -38x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(90 + -38x + 3x2)' equal to zero and attempt to solve: Simplifying 90 + -38x + 3x2 = 0 Solving 90 + -38x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 30 + -12.66666667x + x2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -12.66666667x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -12.66666667x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -12.66666667x + x2 = 0 + -30 -12.66666667x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -12.66666667x + x2 = -30 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 = -30 + 40.11111113 Reorder the terms: 40.11111113 + -12.66666667x + x2 = -30 + 40.11111113 Combine like terms: -30 + 40.11111113 = 10.11111113 40.11111113 + -12.66666667x + x2 = 10.11111113 Factor a perfect square on the left side: (x + -6.333333335)(x + -6.333333335) = 10.11111113 Calculate the square root of the right side: 3.179797341 Break this problem into two subproblems by setting (x + -6.333333335) equal to 3.179797341 and -3.179797341.Subproblem 1
x + -6.333333335 = 3.179797341 Simplifying x + -6.333333335 = 3.179797341 Reorder the terms: -6.333333335 + x = 3.179797341 Solving -6.333333335 + x = 3.179797341 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 = 3.179797341 + 6.333333335 Combine like terms: -6.333333335 + 6.333333335 = 0.000000000 0.000000000 + x = 3.179797341 + 6.333333335 x = 3.179797341 + 6.333333335 Combine like terms: 3.179797341 + 6.333333335 = 9.513130676 x = 9.513130676 Simplifying x = 9.513130676Subproblem 2
x + -6.333333335 = -3.179797341 Simplifying x + -6.333333335 = -3.179797341 Reorder the terms: -6.333333335 + x = -3.179797341 Solving -6.333333335 + x = -3.179797341 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 = -3.179797341 + 6.333333335 Combine like terms: -6.333333335 + 6.333333335 = 0.000000000 0.000000000 + x = -3.179797341 + 6.333333335 x = -3.179797341 + 6.333333335 Combine like terms: -3.179797341 + 6.333333335 = 3.153535994 x = 3.153535994 Simplifying x = 3.153535994Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.513130676, 3.153535994}Solution
x = {9.513130676, 3.153535994}
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