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Simplifying (2x)(3x + -5) = 180 Remove parenthesis around (2x) 2x(3x + -5) = 180 Reorder the terms: 2x(-5 + 3x) = 180 (-5 * 2x + 3x * 2x) = 180 (-10x + 6x2) = 180 Solving -10x + 6x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -10x + 6x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -10x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + -5x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + -5x + 3x2)' equal to zero and attempt to solve: Simplifying -90 + -5x + 3x2 = 0 Solving -90 + -5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -30 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -1.666666667x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -1.666666667x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -1.666666667x + x2 = 0 + 30 -1.666666667x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -1.666666667x + x2 = 30 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 30 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 30 + 0.6944444447 Combine like terms: 30 + 0.6944444447 = 30.6944444447 0.6944444447 + -1.666666667x + x2 = 30.6944444447 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 30.6944444447 Calculate the square root of the right side: 5.540256713 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 5.540256713 and -5.540256713.Subproblem 1
x + -0.8333333335 = 5.540256713 Simplifying x + -0.8333333335 = 5.540256713 Reorder the terms: -0.8333333335 + x = 5.540256713 Solving -0.8333333335 + x = 5.540256713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 5.540256713 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 5.540256713 + 0.8333333335 x = 5.540256713 + 0.8333333335 Combine like terms: 5.540256713 + 0.8333333335 = 6.3735900465 x = 6.3735900465 Simplifying x = 6.3735900465Subproblem 2
x + -0.8333333335 = -5.540256713 Simplifying x + -0.8333333335 = -5.540256713 Reorder the terms: -0.8333333335 + x = -5.540256713 Solving -0.8333333335 + x = -5.540256713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -5.540256713 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -5.540256713 + 0.8333333335 x = -5.540256713 + 0.8333333335 Combine like terms: -5.540256713 + 0.8333333335 = -4.7069233795 x = -4.7069233795 Simplifying x = -4.7069233795Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.3735900465, -4.7069233795}Solution
x = {6.3735900465, -4.7069233795}
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