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Simplifying (x + 4)(x + -17) = x Reorder the terms: (4 + x)(x + -17) = x Reorder the terms: (4 + x)(-17 + x) = x Multiply (4 + x) * (-17 + x) (4(-17 + x) + x(-17 + x)) = x ((-17 * 4 + x * 4) + x(-17 + x)) = x ((-68 + 4x) + x(-17 + x)) = x (-68 + 4x + (-17 * x + x * x)) = x (-68 + 4x + (-17x + x2)) = x Combine like terms: 4x + -17x = -13x (-68 + -13x + x2) = x Solving -68 + -13x + x2 = x Solving for variable 'x'. Reorder the terms: -68 + -13x + -1x + x2 = x + -1x Combine like terms: -13x + -1x = -14x -68 + -14x + x2 = x + -1x Combine like terms: x + -1x = 0 -68 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '68' to each side of the equation. -68 + -14x + 68 + x2 = 0 + 68 Reorder the terms: -68 + 68 + -14x + x2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + -14x + x2 = 0 + 68 -14x + x2 = 0 + 68 Combine like terms: 0 + 68 = 68 -14x + x2 = 68 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 68 + 49 Reorder the terms: 49 + -14x + x2 = 68 + 49 Combine like terms: 68 + 49 = 117 49 + -14x + x2 = 117 Factor a perfect square on the left side: (x + -7)(x + -7) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (x + -7) equal to 10.816653826 and -10.816653826.Subproblem 1
x + -7 = 10.816653826 Simplifying x + -7 = 10.816653826 Reorder the terms: -7 + x = 10.816653826 Solving -7 + x = 10.816653826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 10.816653826 + 7 Combine like terms: -7 + 7 = 0 0 + x = 10.816653826 + 7 x = 10.816653826 + 7 Combine like terms: 10.816653826 + 7 = 17.816653826 x = 17.816653826 Simplifying x = 17.816653826Subproblem 2
x + -7 = -10.816653826 Simplifying x + -7 = -10.816653826 Reorder the terms: -7 + x = -10.816653826 Solving -7 + x = -10.816653826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -10.816653826 + 7 Combine like terms: -7 + 7 = 0 0 + x = -10.816653826 + 7 x = -10.816653826 + 7 Combine like terms: -10.816653826 + 7 = -3.816653826 x = -3.816653826 Simplifying x = -3.816653826Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.816653826, -3.816653826}
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