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Simplifying (x + 4)(x + 4) + -3 = 20 Reorder the terms: (4 + x)(x + 4) + -3 = 20 Reorder the terms: (4 + x)(4 + x) + -3 = 20 Multiply (4 + x) * (4 + x) (4(4 + x) + x(4 + x)) + -3 = 20 ((4 * 4 + x * 4) + x(4 + x)) + -3 = 20 ((16 + 4x) + x(4 + x)) + -3 = 20 (16 + 4x + (4 * x + x * x)) + -3 = 20 (16 + 4x + (4x + x2)) + -3 = 20 Combine like terms: 4x + 4x = 8x (16 + 8x + x2) + -3 = 20 Reorder the terms: 16 + -3 + 8x + x2 = 20 Combine like terms: 16 + -3 = 13 13 + 8x + x2 = 20 Solving 13 + 8x + x2 = 20 Solving for variable 'x'. Reorder the terms: 13 + -20 + 8x + x2 = 20 + -20 Combine like terms: 13 + -20 = -7 -7 + 8x + x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -7 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 8x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 8x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 8x + x2 = 0 + 7 8x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 8x + x2 = 7 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 = 7 + 16 Reorder the terms: 16 + 8x + x2 = 7 + 16 Combine like terms: 7 + 16 = 23 16 + 8x + x2 = 23 Factor a perfect square on the left side: (x + 4)(x + 4) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + 4) equal to 4.795831523 and -4.795831523.Subproblem 1
x + 4 = 4.795831523 Simplifying x + 4 = 4.795831523 Reorder the terms: 4 + x = 4.795831523 Solving 4 + x = 4.795831523 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 = 4.795831523 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.795831523 + -4 x = 4.795831523 + -4 Combine like terms: 4.795831523 + -4 = 0.795831523 x = 0.795831523 Simplifying x = 0.795831523Subproblem 2
x + 4 = -4.795831523 Simplifying x + 4 = -4.795831523 Reorder the terms: 4 + x = -4.795831523 Solving 4 + x = -4.795831523 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 = -4.795831523 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.795831523 + -4 x = -4.795831523 + -4 Combine like terms: -4.795831523 + -4 = -8.795831523 x = -8.795831523 Simplifying x = -8.795831523Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.795831523, -8.795831523}
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