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Simplifying (x + -4)(x + -4) = 769 Reorder the terms: (-4 + x)(x + -4) = 769 Reorder the terms: (-4 + x)(-4 + x) = 769 Multiply (-4 + x) * (-4 + x) (-4(-4 + x) + x(-4 + x)) = 769 ((-4 * -4 + x * -4) + x(-4 + x)) = 769 ((16 + -4x) + x(-4 + x)) = 769 (16 + -4x + (-4 * x + x * x)) = 769 (16 + -4x + (-4x + x2)) = 769 Combine like terms: -4x + -4x = -8x (16 + -8x + x2) = 769 Solving 16 + -8x + x2 = 769 Solving for variable 'x'. Reorder the terms: 16 + -769 + -8x + x2 = 769 + -769 Combine like terms: 16 + -769 = -753 -753 + -8x + x2 = 769 + -769 Combine like terms: 769 + -769 = 0 -753 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '753' to each side of the equation. -753 + -8x + 753 + x2 = 0 + 753 Reorder the terms: -753 + 753 + -8x + x2 = 0 + 753 Combine like terms: -753 + 753 = 0 0 + -8x + x2 = 0 + 753 -8x + x2 = 0 + 753 Combine like terms: 0 + 753 = 753 -8x + x2 = 753 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 753 + 16 Reorder the terms: 16 + -8x + x2 = 753 + 16 Combine like terms: 753 + 16 = 769 16 + -8x + x2 = 769 Factor a perfect square on the left side: (x + -4)(x + -4) = 769 Calculate the square root of the right side: 27.730849248 Break this problem into two subproblems by setting (x + -4) equal to 27.730849248 and -27.730849248.Subproblem 1
x + -4 = 27.730849248 Simplifying x + -4 = 27.730849248 Reorder the terms: -4 + x = 27.730849248 Solving -4 + x = 27.730849248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 27.730849248 + 4 Combine like terms: -4 + 4 = 0 0 + x = 27.730849248 + 4 x = 27.730849248 + 4 Combine like terms: 27.730849248 + 4 = 31.730849248 x = 31.730849248 Simplifying x = 31.730849248Subproblem 2
x + -4 = -27.730849248 Simplifying x + -4 = -27.730849248 Reorder the terms: -4 + x = -27.730849248 Solving -4 + x = -27.730849248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -27.730849248 + 4 Combine like terms: -4 + 4 = 0 0 + x = -27.730849248 + 4 x = -27.730849248 + 4 Combine like terms: -27.730849248 + 4 = -23.730849248 x = -23.730849248 Simplifying x = -23.730849248Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.730849248, -23.730849248}
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