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Simplifying 18x2 + 15x = 27 Reorder the terms: 15x + 18x2 = 27 Solving 15x + 18x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + 15x + 18x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 15x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + 5x + 6x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + 5x + 6x2)' equal to zero and attempt to solve: Simplifying -9 + 5x + 6x2 = 0 Solving -9 + 5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.5 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 0.8333333333x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 0.8333333333x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 0.8333333333x + x2 = 0 + 1.5 0.8333333333x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 0.8333333333x + x2 = 1.5 The x term is 0.8333333333x. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333x + 0.1736111111 + x2 = 1.5 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = 1.5 + 0.1736111111 Combine like terms: 1.5 + 0.1736111111 = 1.6736111111 0.1736111111 + 0.8333333333x + x2 = 1.6736111111 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = 1.6736111111 Calculate the square root of the right side: 1.293681225 Break this problem into two subproblems by setting (x + 0.4166666667) equal to 1.293681225 and -1.293681225.Subproblem 1
x + 0.4166666667 = 1.293681225 Simplifying x + 0.4166666667 = 1.293681225 Reorder the terms: 0.4166666667 + x = 1.293681225 Solving 0.4166666667 + x = 1.293681225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = 1.293681225 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 1.293681225 + -0.4166666667 x = 1.293681225 + -0.4166666667 Combine like terms: 1.293681225 + -0.4166666667 = 0.8770145583 x = 0.8770145583 Simplifying x = 0.8770145583Subproblem 2
x + 0.4166666667 = -1.293681225 Simplifying x + 0.4166666667 = -1.293681225 Reorder the terms: 0.4166666667 + x = -1.293681225 Solving 0.4166666667 + x = -1.293681225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = -1.293681225 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -1.293681225 + -0.4166666667 x = -1.293681225 + -0.4166666667 Combine like terms: -1.293681225 + -0.4166666667 = -1.7103478917 x = -1.7103478917 Simplifying x = -1.7103478917Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8770145583, -1.7103478917}Solution
x = {0.8770145583, -1.7103478917}
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