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Simplifying (x + -4)(x + -7) = 8x + 6 Reorder the terms: (-4 + x)(x + -7) = 8x + 6 Reorder the terms: (-4 + x)(-7 + x) = 8x + 6 Multiply (-4 + x) * (-7 + x) (-4(-7 + x) + x(-7 + x)) = 8x + 6 ((-7 * -4 + x * -4) + x(-7 + x)) = 8x + 6 ((28 + -4x) + x(-7 + x)) = 8x + 6 (28 + -4x + (-7 * x + x * x)) = 8x + 6 (28 + -4x + (-7x + x2)) = 8x + 6 Combine like terms: -4x + -7x = -11x (28 + -11x + x2) = 8x + 6 Reorder the terms: 28 + -11x + x2 = 6 + 8x Solving 28 + -11x + x2 = 6 + 8x Solving for variable 'x'. Reorder the terms: 28 + -6 + -11x + -8x + x2 = 6 + 8x + -6 + -8x Combine like terms: 28 + -6 = 22 22 + -11x + -8x + x2 = 6 + 8x + -6 + -8x Combine like terms: -11x + -8x = -19x 22 + -19x + x2 = 6 + 8x + -6 + -8x Reorder the terms: 22 + -19x + x2 = 6 + -6 + 8x + -8x Combine like terms: 6 + -6 = 0 22 + -19x + x2 = 0 + 8x + -8x 22 + -19x + x2 = 8x + -8x Combine like terms: 8x + -8x = 0 22 + -19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + -19x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + -19x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -19x + x2 = 0 + -22 -19x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 -19x + x2 = -22 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -22 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -22 + 90.25 Combine like terms: -22 + 90.25 = 68.25 90.25 + -19x + x2 = 68.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 68.25 Calculate the square root of the right side: 8.261355821 Break this problem into two subproblems by setting (x + -9.5) equal to 8.261355821 and -8.261355821.Subproblem 1
x + -9.5 = 8.261355821 Simplifying x + -9.5 = 8.261355821 Reorder the terms: -9.5 + x = 8.261355821 Solving -9.5 + x = 8.261355821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 8.261355821 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 8.261355821 + 9.5 x = 8.261355821 + 9.5 Combine like terms: 8.261355821 + 9.5 = 17.761355821 x = 17.761355821 Simplifying x = 17.761355821Subproblem 2
x + -9.5 = -8.261355821 Simplifying x + -9.5 = -8.261355821 Reorder the terms: -9.5 + x = -8.261355821 Solving -9.5 + x = -8.261355821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -8.261355821 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -8.261355821 + 9.5 x = -8.261355821 + 9.5 Combine like terms: -8.261355821 + 9.5 = 1.238644179 x = 1.238644179 Simplifying x = 1.238644179Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.761355821, 1.238644179}
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