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Simplifying 18x2 + -15x + -45 = 0 Reorder the terms: -45 + -15x + 18x2 = 0 Solving -45 + -15x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + -5x + 6x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-15 + -5x + 6x2)' equal to zero and attempt to solve: Simplifying -15 + -5x + 6x2 = 0 Solving -15 + -5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.5 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -0.8333333333x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -0.8333333333x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -0.8333333333x + x2 = 0 + 2.5 -0.8333333333x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -0.8333333333x + x2 = 2.5 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 = 2.5 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = 2.5 + 0.1736111111 Combine like terms: 2.5 + 0.1736111111 = 2.6736111111 0.1736111111 + -0.8333333333x + x2 = 2.6736111111 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = 2.6736111111 Calculate the square root of the right side: 1.635118073 Break this problem into two subproblems by setting (x + -0.4166666667) equal to 1.635118073 and -1.635118073.Subproblem 1
x + -0.4166666667 = 1.635118073 Simplifying x + -0.4166666667 = 1.635118073 Reorder the terms: -0.4166666667 + x = 1.635118073 Solving -0.4166666667 + x = 1.635118073 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 = 1.635118073 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = 1.635118073 + 0.4166666667 x = 1.635118073 + 0.4166666667 Combine like terms: 1.635118073 + 0.4166666667 = 2.0517847397 x = 2.0517847397 Simplifying x = 2.0517847397Subproblem 2
x + -0.4166666667 = -1.635118073 Simplifying x + -0.4166666667 = -1.635118073 Reorder the terms: -0.4166666667 + x = -1.635118073 Solving -0.4166666667 + x = -1.635118073 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 = -1.635118073 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = -1.635118073 + 0.4166666667 x = -1.635118073 + 0.4166666667 Combine like terms: -1.635118073 + 0.4166666667 = -1.2184514063 x = -1.2184514063 Simplifying x = -1.2184514063Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0517847397, -1.2184514063}Solution
x = {2.0517847397, -1.2184514063}
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