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Simplifying 6x2 + -108x + 156 = 0 Reorder the terms: 156 + -108x + 6x2 = 0 Solving 156 + -108x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(26 + -18x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(26 + -18x + x2)' equal to zero and attempt to solve: Simplifying 26 + -18x + x2 = 0 Solving 26 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + -18x + -26 + x2 = 0 + -26 Reorder the terms: 26 + -26 + -18x + x2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -18x + x2 = 0 + -26 -18x + x2 = 0 + -26 Combine like terms: 0 + -26 = -26 -18x + x2 = -26 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -26 + 81 Reorder the terms: 81 + -18x + x2 = -26 + 81 Combine like terms: -26 + 81 = 55 81 + -18x + x2 = 55 Factor a perfect square on the left side: (x + -9)(x + -9) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (x + -9) equal to 7.416198487 and -7.416198487.Subproblem 1
x + -9 = 7.416198487 Simplifying x + -9 = 7.416198487 Reorder the terms: -9 + x = 7.416198487 Solving -9 + x = 7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 7.416198487 + 9 Combine like terms: -9 + 9 = 0 0 + x = 7.416198487 + 9 x = 7.416198487 + 9 Combine like terms: 7.416198487 + 9 = 16.416198487 x = 16.416198487 Simplifying x = 16.416198487Subproblem 2
x + -9 = -7.416198487 Simplifying x + -9 = -7.416198487 Reorder the terms: -9 + x = -7.416198487 Solving -9 + x = -7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -7.416198487 + 9 Combine like terms: -9 + 9 = 0 0 + x = -7.416198487 + 9 x = -7.416198487 + 9 Combine like terms: -7.416198487 + 9 = 1.583801513 x = 1.583801513 Simplifying x = 1.583801513Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.416198487, 1.583801513}Solution
x = {16.416198487, 1.583801513}
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