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Simplifying (x + -4)(x + -4) = 69 Reorder the terms: (-4 + x)(x + -4) = 69 Reorder the terms: (-4 + x)(-4 + x) = 69 Multiply (-4 + x) * (-4 + x) (-4(-4 + x) + x(-4 + x)) = 69 ((-4 * -4 + x * -4) + x(-4 + x)) = 69 ((16 + -4x) + x(-4 + x)) = 69 (16 + -4x + (-4 * x + x * x)) = 69 (16 + -4x + (-4x + x2)) = 69 Combine like terms: -4x + -4x = -8x (16 + -8x + x2) = 69 Solving 16 + -8x + x2 = 69 Solving for variable 'x'. Reorder the terms: 16 + -69 + -8x + x2 = 69 + -69 Combine like terms: 16 + -69 = -53 -53 + -8x + x2 = 69 + -69 Combine like terms: 69 + -69 = 0 -53 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + -8x + 53 + x2 = 0 + 53 Reorder the terms: -53 + 53 + -8x + x2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + -8x + x2 = 0 + 53 -8x + x2 = 0 + 53 Combine like terms: 0 + 53 = 53 -8x + x2 = 53 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 = 53 + 16 Reorder the terms: 16 + -8x + x2 = 53 + 16 Combine like terms: 53 + 16 = 69 16 + -8x + x2 = 69 Factor a perfect square on the left side: (x + -4)(x + -4) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (x + -4) equal to 8.306623863 and -8.306623863.Subproblem 1
x + -4 = 8.306623863 Simplifying x + -4 = 8.306623863 Reorder the terms: -4 + x = 8.306623863 Solving -4 + x = 8.306623863 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 = 8.306623863 + 4 Combine like terms: -4 + 4 = 0 0 + x = 8.306623863 + 4 x = 8.306623863 + 4 Combine like terms: 8.306623863 + 4 = 12.306623863 x = 12.306623863 Simplifying x = 12.306623863Subproblem 2
x + -4 = -8.306623863 Simplifying x + -4 = -8.306623863 Reorder the terms: -4 + x = -8.306623863 Solving -4 + x = -8.306623863 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 = -8.306623863 + 4 Combine like terms: -4 + 4 = 0 0 + x = -8.306623863 + 4 x = -8.306623863 + 4 Combine like terms: -8.306623863 + 4 = -4.306623863 x = -4.306623863 Simplifying x = -4.306623863Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.306623863, -4.306623863}
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