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Simplifying 27x2 + 42x + -9 = 0 Reorder the terms: -9 + 42x + 27x2 = 0 Solving -9 + 42x + 27x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 14x + 9x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + 14x + 9x2)' equal to zero and attempt to solve: Simplifying -3 + 14x + 9x2 = 0 Solving -3 + 14x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.3333333333 + 1.555555556x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.555555556x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.555555556x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.555555556x + x2 = 0 + 0.3333333333 1.555555556x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 1.555555556x + x2 = 0.3333333333 The x term is 1.555555556x. Take half its coefficient (0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. 1.555555556x + 0.6049382720 + x2 = 0.3333333333 + 0.6049382720 Reorder the terms: 0.6049382720 + 1.555555556x + x2 = 0.3333333333 + 0.6049382720 Combine like terms: 0.3333333333 + 0.6049382720 = 0.9382716053 0.6049382720 + 1.555555556x + x2 = 0.9382716053 Factor a perfect square on the left side: (x + 0.777777778)(x + 0.777777778) = 0.9382716053 Calculate the square root of the right side: 0.96864421 Break this problem into two subproblems by setting (x + 0.777777778) equal to 0.96864421 and -0.96864421.Subproblem 1
x + 0.777777778 = 0.96864421 Simplifying x + 0.777777778 = 0.96864421 Reorder the terms: 0.777777778 + x = 0.96864421 Solving 0.777777778 + x = 0.96864421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = 0.96864421 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = 0.96864421 + -0.777777778 x = 0.96864421 + -0.777777778 Combine like terms: 0.96864421 + -0.777777778 = 0.190866432 x = 0.190866432 Simplifying x = 0.190866432Subproblem 2
x + 0.777777778 = -0.96864421 Simplifying x + 0.777777778 = -0.96864421 Reorder the terms: 0.777777778 + x = -0.96864421 Solving 0.777777778 + x = -0.96864421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = -0.96864421 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = -0.96864421 + -0.777777778 x = -0.96864421 + -0.777777778 Combine like terms: -0.96864421 + -0.777777778 = -1.746421988 x = -1.746421988 Simplifying x = -1.746421988Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.190866432, -1.746421988}Solution
x = {0.190866432, -1.746421988}
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