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Simplifying (15x + -48)(5x + 12) = 40 Reorder the terms: (-48 + 15x)(5x + 12) = 40 Reorder the terms: (-48 + 15x)(12 + 5x) = 40 Multiply (-48 + 15x) * (12 + 5x) (-48(12 + 5x) + 15x * (12 + 5x)) = 40 ((12 * -48 + 5x * -48) + 15x * (12 + 5x)) = 40 ((-576 + -240x) + 15x * (12 + 5x)) = 40 (-576 + -240x + (12 * 15x + 5x * 15x)) = 40 (-576 + -240x + (180x + 75x2)) = 40 Combine like terms: -240x + 180x = -60x (-576 + -60x + 75x2) = 40 Solving -576 + -60x + 75x2 = 40 Solving for variable 'x'. Reorder the terms: -576 + -40 + -60x + 75x2 = 40 + -40 Combine like terms: -576 + -40 = -616 -616 + -60x + 75x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -616 + -60x + 75x2 = 0 Begin completing the square. Divide all terms by 75 the coefficient of the squared term: Divide each side by '75'. -8.213333333 + -0.8x + x2 = 0 Move the constant term to the right: Add '8.213333333' to each side of the equation. -8.213333333 + -0.8x + 8.213333333 + x2 = 0 + 8.213333333 Reorder the terms: -8.213333333 + 8.213333333 + -0.8x + x2 = 0 + 8.213333333 Combine like terms: -8.213333333 + 8.213333333 = 0.000000000 0.000000000 + -0.8x + x2 = 0 + 8.213333333 -0.8x + x2 = 0 + 8.213333333 Combine like terms: 0 + 8.213333333 = 8.213333333 -0.8x + x2 = 8.213333333 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 8.213333333 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 8.213333333 + 0.16 Combine like terms: 8.213333333 + 0.16 = 8.373333333 0.16 + -0.8x + x2 = 8.373333333 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 8.373333333 Calculate the square root of the right side: 2.893671255 Break this problem into two subproblems by setting (x + -0.4) equal to 2.893671255 and -2.893671255.Subproblem 1
x + -0.4 = 2.893671255 Simplifying x + -0.4 = 2.893671255 Reorder the terms: -0.4 + x = 2.893671255 Solving -0.4 + x = 2.893671255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 2.893671255 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 2.893671255 + 0.4 x = 2.893671255 + 0.4 Combine like terms: 2.893671255 + 0.4 = 3.293671255 x = 3.293671255 Simplifying x = 3.293671255Subproblem 2
x + -0.4 = -2.893671255 Simplifying x + -0.4 = -2.893671255 Reorder the terms: -0.4 + x = -2.893671255 Solving -0.4 + x = -2.893671255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -2.893671255 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -2.893671255 + 0.4 x = -2.893671255 + 0.4 Combine like terms: -2.893671255 + 0.4 = -2.493671255 x = -2.493671255 Simplifying x = -2.493671255Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.293671255, -2.493671255}
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