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Simplifying (6x + 5)(5x + -12) = 180 Reorder the terms: (5 + 6x)(5x + -12) = 180 Reorder the terms: (5 + 6x)(-12 + 5x) = 180 Multiply (5 + 6x) * (-12 + 5x) (5(-12 + 5x) + 6x * (-12 + 5x)) = 180 ((-12 * 5 + 5x * 5) + 6x * (-12 + 5x)) = 180 ((-60 + 25x) + 6x * (-12 + 5x)) = 180 (-60 + 25x + (-12 * 6x + 5x * 6x)) = 180 (-60 + 25x + (-72x + 30x2)) = 180 Combine like terms: 25x + -72x = -47x (-60 + -47x + 30x2) = 180 Solving -60 + -47x + 30x2 = 180 Solving for variable 'x'. Reorder the terms: -60 + -180 + -47x + 30x2 = 180 + -180 Combine like terms: -60 + -180 = -240 -240 + -47x + 30x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -240 + -47x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -8 + -1.566666667x + x2 = 0.0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -1.566666667x + 8 + x2 = 0.0 + 8 Reorder the terms: -8 + 8 + -1.566666667x + x2 = 0.0 + 8 Combine like terms: -8 + 8 = 0 0 + -1.566666667x + x2 = 0.0 + 8 -1.566666667x + x2 = 0.0 + 8 Combine like terms: 0.0 + 8 = 8 -1.566666667x + x2 = 8 The x term is -1.566666667x. Take half its coefficient (-0.7833333335). Square it (0.6136111114) and add it to both sides. Add '0.6136111114' to each side of the equation. -1.566666667x + 0.6136111114 + x2 = 8 + 0.6136111114 Reorder the terms: 0.6136111114 + -1.566666667x + x2 = 8 + 0.6136111114 Combine like terms: 8 + 0.6136111114 = 8.6136111114 0.6136111114 + -1.566666667x + x2 = 8.6136111114 Factor a perfect square on the left side: (x + -0.7833333335)(x + -0.7833333335) = 8.6136111114 Calculate the square root of the right side: 2.934895417 Break this problem into two subproblems by setting (x + -0.7833333335) equal to 2.934895417 and -2.934895417.Subproblem 1
x + -0.7833333335 = 2.934895417 Simplifying x + -0.7833333335 = 2.934895417 Reorder the terms: -0.7833333335 + x = 2.934895417 Solving -0.7833333335 + x = 2.934895417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7833333335' to each side of the equation. -0.7833333335 + 0.7833333335 + x = 2.934895417 + 0.7833333335 Combine like terms: -0.7833333335 + 0.7833333335 = 0.0000000000 0.0000000000 + x = 2.934895417 + 0.7833333335 x = 2.934895417 + 0.7833333335 Combine like terms: 2.934895417 + 0.7833333335 = 3.7182287505 x = 3.7182287505 Simplifying x = 3.7182287505Subproblem 2
x + -0.7833333335 = -2.934895417 Simplifying x + -0.7833333335 = -2.934895417 Reorder the terms: -0.7833333335 + x = -2.934895417 Solving -0.7833333335 + x = -2.934895417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7833333335' to each side of the equation. -0.7833333335 + 0.7833333335 + x = -2.934895417 + 0.7833333335 Combine like terms: -0.7833333335 + 0.7833333335 = 0.0000000000 0.0000000000 + x = -2.934895417 + 0.7833333335 x = -2.934895417 + 0.7833333335 Combine like terms: -2.934895417 + 0.7833333335 = -2.1515620835 x = -2.1515620835 Simplifying x = -2.1515620835Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.7182287505, -2.1515620835}
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