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Simplifying 36x2 + -84x + 9 = 0 Reorder the terms: 9 + -84x + 36x2 = 0 Solving 9 + -84x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -28x + 12x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -28x + 12x2)' equal to zero and attempt to solve: Simplifying 3 + -28x + 12x2 = 0 Solving 3 + -28x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.25 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -2.333333333x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -2.333333333x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -2.333333333x + x2 = 0 + -0.25 -2.333333333x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -2.333333333x + x2 = -0.25 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = -0.25 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = -0.25 + 1.361111112 Combine like terms: -0.25 + 1.361111112 = 1.111111112 1.361111112 + -2.333333333x + x2 = 1.111111112 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 1.111111112 Calculate the square root of the right side: 1.054092554 Break this problem into two subproblems by setting (x + -1.166666667) equal to 1.054092554 and -1.054092554.Subproblem 1
x + -1.166666667 = 1.054092554 Simplifying x + -1.166666667 = 1.054092554 Reorder the terms: -1.166666667 + x = 1.054092554 Solving -1.166666667 + x = 1.054092554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 1.054092554 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 1.054092554 + 1.166666667 x = 1.054092554 + 1.166666667 Combine like terms: 1.054092554 + 1.166666667 = 2.220759221 x = 2.220759221 Simplifying x = 2.220759221Subproblem 2
x + -1.166666667 = -1.054092554 Simplifying x + -1.166666667 = -1.054092554 Reorder the terms: -1.166666667 + x = -1.054092554 Solving -1.166666667 + x = -1.054092554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -1.054092554 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -1.054092554 + 1.166666667 x = -1.054092554 + 1.166666667 Combine like terms: -1.054092554 + 1.166666667 = 0.112574113 x = 0.112574113 Simplifying x = 0.112574113Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.220759221, 0.112574113}Solution
x = {2.220759221, 0.112574113}
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