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Simplifying 18x2 + 42x + -20 = 0 Reorder the terms: -20 + 42x + 18x2 = 0 Solving -20 + 42x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 21x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + 21x + 9x2)' equal to zero and attempt to solve: Simplifying -10 + 21x + 9x2 = 0 Solving -10 + 21x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + 2.333333333x + 1.111111111 + x2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + 2.333333333x + x2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + 2.333333333x + x2 = 0 + 1.111111111 2.333333333x + x2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 2.333333333x + x2 = 1.111111111 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 = 1.111111111 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 1.111111111 + 1.361111112 Combine like terms: 1.111111111 + 1.361111112 = 2.472222223 1.361111112 + 2.333333333x + x2 = 2.472222223 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 2.472222223 Calculate the square root of the right side: 1.572330189 Break this problem into two subproblems by setting (x + 1.166666667) equal to 1.572330189 and -1.572330189.Subproblem 1
x + 1.166666667 = 1.572330189 Simplifying x + 1.166666667 = 1.572330189 Reorder the terms: 1.166666667 + x = 1.572330189 Solving 1.166666667 + x = 1.572330189 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 = 1.572330189 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 1.572330189 + -1.166666667 x = 1.572330189 + -1.166666667 Combine like terms: 1.572330189 + -1.166666667 = 0.405663522 x = 0.405663522 Simplifying x = 0.405663522Subproblem 2
x + 1.166666667 = -1.572330189 Simplifying x + 1.166666667 = -1.572330189 Reorder the terms: 1.166666667 + x = -1.572330189 Solving 1.166666667 + x = -1.572330189 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 = -1.572330189 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -1.572330189 + -1.166666667 x = -1.572330189 + -1.166666667 Combine like terms: -1.572330189 + -1.166666667 = -2.738996856 x = -2.738996856 Simplifying x = -2.738996856Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.405663522, -2.738996856}Solution
x = {0.405663522, -2.738996856}
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