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Simplifying (3x)(5x + -48) = 180 Remove parenthesis around (3x) 3x(5x + -48) = 180 Reorder the terms: 3x(-48 + 5x) = 180 (-48 * 3x + 5x * 3x) = 180 (-144x + 15x2) = 180 Solving -144x + 15x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -144x + 15x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -144x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-60 + -48x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-60 + -48x + 5x2)' equal to zero and attempt to solve: Simplifying -60 + -48x + 5x2 = 0 Solving -60 + -48x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12 + -9.6x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -9.6x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -9.6x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -9.6x + x2 = 0 + 12 -9.6x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -9.6x + x2 = 12 The x term is -9.6x. Take half its coefficient (-4.8). Square it (23.04) and add it to both sides. Add '23.04' to each side of the equation. -9.6x + 23.04 + x2 = 12 + 23.04 Reorder the terms: 23.04 + -9.6x + x2 = 12 + 23.04 Combine like terms: 12 + 23.04 = 35.04 23.04 + -9.6x + x2 = 35.04 Factor a perfect square on the left side: (x + -4.8)(x + -4.8) = 35.04 Calculate the square root of the right side: 5.919459435 Break this problem into two subproblems by setting (x + -4.8) equal to 5.919459435 and -5.919459435.Subproblem 1
x + -4.8 = 5.919459435 Simplifying x + -4.8 = 5.919459435 Reorder the terms: -4.8 + x = 5.919459435 Solving -4.8 + x = 5.919459435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = 5.919459435 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = 5.919459435 + 4.8 x = 5.919459435 + 4.8 Combine like terms: 5.919459435 + 4.8 = 10.719459435 x = 10.719459435 Simplifying x = 10.719459435Subproblem 2
x + -4.8 = -5.919459435 Simplifying x + -4.8 = -5.919459435 Reorder the terms: -4.8 + x = -5.919459435 Solving -4.8 + x = -5.919459435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = -5.919459435 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = -5.919459435 + 4.8 x = -5.919459435 + 4.8 Combine like terms: -5.919459435 + 4.8 = -1.119459435 x = -1.119459435 Simplifying x = -1.119459435Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.719459435, -1.119459435}Solution
x = {10.719459435, -1.119459435}
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