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Simplifying 3x(5x + -240) = 15 Reorder the terms: 3x(-240 + 5x) = 15 (-240 * 3x + 5x * 3x) = 15 (-720x + 15x2) = 15 Solving -720x + 15x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + -720x + 15x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -720x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(-1 + -48x + x2) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-1 + -48x + x2)' equal to zero and attempt to solve: Simplifying -1 + -48x + x2 = 0 Solving -1 + -48x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -48x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -48x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -48x + x2 = 0 + 1 -48x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -48x + x2 = 1 The x term is -48x. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48x + 576 + x2 = 1 + 576 Reorder the terms: 576 + -48x + x2 = 1 + 576 Combine like terms: 1 + 576 = 577 576 + -48x + x2 = 577 Factor a perfect square on the left side: (x + -24)(x + -24) = 577 Calculate the square root of the right side: 24.020824299 Break this problem into two subproblems by setting (x + -24) equal to 24.020824299 and -24.020824299.Subproblem 1
x + -24 = 24.020824299 Simplifying x + -24 = 24.020824299 Reorder the terms: -24 + x = 24.020824299 Solving -24 + x = 24.020824299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = 24.020824299 + 24 Combine like terms: -24 + 24 = 0 0 + x = 24.020824299 + 24 x = 24.020824299 + 24 Combine like terms: 24.020824299 + 24 = 48.020824299 x = 48.020824299 Simplifying x = 48.020824299Subproblem 2
x + -24 = -24.020824299 Simplifying x + -24 = -24.020824299 Reorder the terms: -24 + x = -24.020824299 Solving -24 + x = -24.020824299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = -24.020824299 + 24 Combine like terms: -24 + 24 = 0 0 + x = -24.020824299 + 24 x = -24.020824299 + 24 Combine like terms: -24.020824299 + 24 = -0.020824299 x = -0.020824299 Simplifying x = -0.020824299Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.020824299, -0.020824299}Solution
x = {48.020824299, -0.020824299}
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