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Simplifying (x + -12)(x + 20) = x Reorder the terms: (-12 + x)(x + 20) = x Reorder the terms: (-12 + x)(20 + x) = x Multiply (-12 + x) * (20 + x) (-12(20 + x) + x(20 + x)) = x ((20 * -12 + x * -12) + x(20 + x)) = x ((-240 + -12x) + x(20 + x)) = x (-240 + -12x + (20 * x + x * x)) = x (-240 + -12x + (20x + x2)) = x Combine like terms: -12x + 20x = 8x (-240 + 8x + x2) = x Solving -240 + 8x + x2 = x Solving for variable 'x'. Reorder the terms: -240 + 8x + -1x + x2 = x + -1x Combine like terms: 8x + -1x = 7x -240 + 7x + x2 = x + -1x Combine like terms: x + -1x = 0 -240 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 7x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + 7x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 7x + x2 = 0 + 240 7x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 7x + x2 = 240 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 240 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 240 + 12.25 Combine like terms: 240 + 12.25 = 252.25 12.25 + 7x + x2 = 252.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 252.25 Calculate the square root of the right side: 15.882380174 Break this problem into two subproblems by setting (x + 3.5) equal to 15.882380174 and -15.882380174.Subproblem 1
x + 3.5 = 15.882380174 Simplifying x + 3.5 = 15.882380174 Reorder the terms: 3.5 + x = 15.882380174 Solving 3.5 + x = 15.882380174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 15.882380174 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 15.882380174 + -3.5 x = 15.882380174 + -3.5 Combine like terms: 15.882380174 + -3.5 = 12.382380174 x = 12.382380174 Simplifying x = 12.382380174Subproblem 2
x + 3.5 = -15.882380174 Simplifying x + 3.5 = -15.882380174 Reorder the terms: 3.5 + x = -15.882380174 Solving 3.5 + x = -15.882380174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -15.882380174 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -15.882380174 + -3.5 x = -15.882380174 + -3.5 Combine like terms: -15.882380174 + -3.5 = -19.382380174 x = -19.382380174 Simplifying x = -19.382380174Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.382380174, -19.382380174}
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