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Simplifying 2x(6x + -5) = 6 Reorder the terms: 2x(-5 + 6x) = 6 (-5 * 2x + 6x * 2x) = 6 (-10x + 12x2) = 6 Solving -10x + 12x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + -10x + 12x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -10x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -5x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -5x + 6x2)' equal to zero and attempt to solve: Simplifying -3 + -5x + 6x2 = 0 Solving -3 + -5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.8333333333x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.8333333333x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.8333333333x + x2 = 0 + 0.5 -0.8333333333x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.8333333333x + x2 = 0.5 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 = 0.5 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = 0.5 + 0.1736111111 Combine like terms: 0.5 + 0.1736111111 = 0.6736111111 0.1736111111 + -0.8333333333x + x2 = 0.6736111111 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = 0.6736111111 Calculate the square root of the right side: 0.82073815 Break this problem into two subproblems by setting (x + -0.4166666667) equal to 0.82073815 and -0.82073815.Subproblem 1
x + -0.4166666667 = 0.82073815 Simplifying x + -0.4166666667 = 0.82073815 Reorder the terms: -0.4166666667 + x = 0.82073815 Solving -0.4166666667 + x = 0.82073815 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 = 0.82073815 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = 0.82073815 + 0.4166666667 x = 0.82073815 + 0.4166666667 Combine like terms: 0.82073815 + 0.4166666667 = 1.2374048167 x = 1.2374048167 Simplifying x = 1.2374048167Subproblem 2
x + -0.4166666667 = -0.82073815 Simplifying x + -0.4166666667 = -0.82073815 Reorder the terms: -0.4166666667 + x = -0.82073815 Solving -0.4166666667 + x = -0.82073815 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 = -0.82073815 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = -0.82073815 + 0.4166666667 x = -0.82073815 + 0.4166666667 Combine like terms: -0.82073815 + 0.4166666667 = -0.4040714833 x = -0.4040714833 Simplifying x = -0.4040714833Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2374048167, -0.4040714833}Solution
x = {1.2374048167, -0.4040714833}
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