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Simplifying (x + -4)(x + -4) = 6.25 Reorder the terms: (-4 + x)(x + -4) = 6.25 Reorder the terms: (-4 + x)(-4 + x) = 6.25 Multiply (-4 + x) * (-4 + x) (-4(-4 + x) + x(-4 + x)) = 6.25 ((-4 * -4 + x * -4) + x(-4 + x)) = 6.25 ((16 + -4x) + x(-4 + x)) = 6.25 (16 + -4x + (-4 * x + x * x)) = 6.25 (16 + -4x + (-4x + x2)) = 6.25 Combine like terms: -4x + -4x = -8x (16 + -8x + x2) = 6.25 Solving 16 + -8x + x2 = 6.25 Solving for variable 'x'. Reorder the terms: 16 + -6.25 + -8x + x2 = 6.25 + -6.25 Combine like terms: 16 + -6.25 = 9.75 9.75 + -8x + x2 = 6.25 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 9.75 + -8x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-9.75' to each side of the equation. 9.75 + -8x + -9.75 + x2 = 0.00 + -9.75 Reorder the terms: 9.75 + -9.75 + -8x + x2 = 0.00 + -9.75 Combine like terms: 9.75 + -9.75 = 0.00 0.00 + -8x + x2 = 0.00 + -9.75 -8x + x2 = 0.00 + -9.75 Combine like terms: 0.00 + -9.75 = -9.75 -8x + x2 = -9.75 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 = -9.75 + 16 Reorder the terms: 16 + -8x + x2 = -9.75 + 16 Combine like terms: -9.75 + 16 = 6.25 16 + -8x + x2 = 6.25 Factor a perfect square on the left side: (x + -4)(x + -4) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (x + -4) equal to 2.5 and -2.5.Subproblem 1
x + -4 = 2.5 Simplifying x + -4 = 2.5 Reorder the terms: -4 + x = 2.5 Solving -4 + x = 2.5 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 = 2.5 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.5 + 4 x = 2.5 + 4 Combine like terms: 2.5 + 4 = 6.5 x = 6.5 Simplifying x = 6.5Subproblem 2
x + -4 = -2.5 Simplifying x + -4 = -2.5 Reorder the terms: -4 + x = -2.5 Solving -4 + x = -2.5 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 = -2.5 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.5 + 4 x = -2.5 + 4 Combine like terms: -2.5 + 4 = 1.5 x = 1.5 Simplifying x = 1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.5, 1.5}
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