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Simplifying -36x2 + 84x + -14 = 0 Reorder the terms: -14 + 84x + -36x2 = 0 Solving -14 + 84x + -36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 42x + -18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 42x + -18x2)' equal to zero and attempt to solve: Simplifying -7 + 42x + -18x2 = 0 Solving -7 + 42x + -18x2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. 0.3888888889 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '-0.3888888889' to each side of the equation. 0.3888888889 + -2.333333333x + -0.3888888889 + x2 = 0 + -0.3888888889 Reorder the terms: 0.3888888889 + -0.3888888889 + -2.333333333x + x2 = 0 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + -2.333333333x + x2 = 0 + -0.3888888889 -2.333333333x + x2 = 0 + -0.3888888889 Combine like terms: 0 + -0.3888888889 = -0.3888888889 -2.333333333x + x2 = -0.3888888889 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 = -0.3888888889 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = -0.3888888889 + 1.361111112 Combine like terms: -0.3888888889 + 1.361111112 = 0.9722222231 1.361111112 + -2.333333333x + x2 = 0.9722222231 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 0.9722222231 Calculate the square root of the right side: 0.986013298 Break this problem into two subproblems by setting (x + -1.166666667) equal to 0.986013298 and -0.986013298.Subproblem 1
x + -1.166666667 = 0.986013298 Simplifying x + -1.166666667 = 0.986013298 Reorder the terms: -1.166666667 + x = 0.986013298 Solving -1.166666667 + x = 0.986013298 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 = 0.986013298 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 0.986013298 + 1.166666667 x = 0.986013298 + 1.166666667 Combine like terms: 0.986013298 + 1.166666667 = 2.152679965 x = 2.152679965 Simplifying x = 2.152679965Subproblem 2
x + -1.166666667 = -0.986013298 Simplifying x + -1.166666667 = -0.986013298 Reorder the terms: -1.166666667 + x = -0.986013298 Solving -1.166666667 + x = -0.986013298 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 = -0.986013298 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -0.986013298 + 1.166666667 x = -0.986013298 + 1.166666667 Combine like terms: -0.986013298 + 1.166666667 = 0.180653369 x = 0.180653369 Simplifying x = 0.180653369Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.152679965, 0.180653369}Solution
x = {2.152679965, 0.180653369}
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