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Simplifying (x + 4)(x + -15) = 16x Reorder the terms: (4 + x)(x + -15) = 16x Reorder the terms: (4 + x)(-15 + x) = 16x Multiply (4 + x) * (-15 + x) (4(-15 + x) + x(-15 + x)) = 16x ((-15 * 4 + x * 4) + x(-15 + x)) = 16x ((-60 + 4x) + x(-15 + x)) = 16x (-60 + 4x + (-15 * x + x * x)) = 16x (-60 + 4x + (-15x + x2)) = 16x Combine like terms: 4x + -15x = -11x (-60 + -11x + x2) = 16x Solving -60 + -11x + x2 = 16x Solving for variable 'x'. Reorder the terms: -60 + -11x + -16x + x2 = 16x + -16x Combine like terms: -11x + -16x = -27x -60 + -27x + x2 = 16x + -16x Combine like terms: 16x + -16x = 0 -60 + -27x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -27x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -27x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -27x + x2 = 0 + 60 -27x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -27x + x2 = 60 The x term is -27x. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27x + 182.25 + x2 = 60 + 182.25 Reorder the terms: 182.25 + -27x + x2 = 60 + 182.25 Combine like terms: 60 + 182.25 = 242.25 182.25 + -27x + x2 = 242.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 242.25 Calculate the square root of the right side: 15.564382416 Break this problem into two subproblems by setting (x + -13.5) equal to 15.564382416 and -15.564382416.Subproblem 1
x + -13.5 = 15.564382416 Simplifying x + -13.5 = 15.564382416 Reorder the terms: -13.5 + x = 15.564382416 Solving -13.5 + x = 15.564382416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = 15.564382416 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 15.564382416 + 13.5 x = 15.564382416 + 13.5 Combine like terms: 15.564382416 + 13.5 = 29.064382416 x = 29.064382416 Simplifying x = 29.064382416Subproblem 2
x + -13.5 = -15.564382416 Simplifying x + -13.5 = -15.564382416 Reorder the terms: -13.5 + x = -15.564382416 Solving -13.5 + x = -15.564382416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = -15.564382416 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -15.564382416 + 13.5 x = -15.564382416 + 13.5 Combine like terms: -15.564382416 + 13.5 = -2.064382416 x = -2.064382416 Simplifying x = -2.064382416Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.064382416, -2.064382416}
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