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Simplifying (x + 4)(x + -16) = 6x Reorder the terms: (4 + x)(x + -16) = 6x Reorder the terms: (4 + x)(-16 + x) = 6x Multiply (4 + x) * (-16 + x) (4(-16 + x) + x(-16 + x)) = 6x ((-16 * 4 + x * 4) + x(-16 + x)) = 6x ((-64 + 4x) + x(-16 + x)) = 6x (-64 + 4x + (-16 * x + x * x)) = 6x (-64 + 4x + (-16x + x2)) = 6x Combine like terms: 4x + -16x = -12x (-64 + -12x + x2) = 6x Solving -64 + -12x + x2 = 6x Solving for variable 'x'. Reorder the terms: -64 + -12x + -6x + x2 = 6x + -6x Combine like terms: -12x + -6x = -18x -64 + -18x + x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -64 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -18x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + -18x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -18x + x2 = 0 + 64 -18x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 -18x + x2 = 64 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 64 + 81 Reorder the terms: 81 + -18x + x2 = 64 + 81 Combine like terms: 64 + 81 = 145 81 + -18x + x2 = 145 Factor a perfect square on the left side: (x + -9)(x + -9) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (x + -9) equal to 12.041594579 and -12.041594579.Subproblem 1
x + -9 = 12.041594579 Simplifying x + -9 = 12.041594579 Reorder the terms: -9 + x = 12.041594579 Solving -9 + x = 12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 12.041594579 + 9 Combine like terms: -9 + 9 = 0 0 + x = 12.041594579 + 9 x = 12.041594579 + 9 Combine like terms: 12.041594579 + 9 = 21.041594579 x = 21.041594579 Simplifying x = 21.041594579Subproblem 2
x + -9 = -12.041594579 Simplifying x + -9 = -12.041594579 Reorder the terms: -9 + x = -12.041594579 Solving -9 + x = -12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -12.041594579 + 9 Combine like terms: -9 + 9 = 0 0 + x = -12.041594579 + 9 x = -12.041594579 + 9 Combine like terms: -12.041594579 + 9 = -3.041594579 x = -3.041594579 Simplifying x = -3.041594579Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.041594579, -3.041594579}
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