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Simplifying (x + 4)(x + -7) = 5x Reorder the terms: (4 + x)(x + -7) = 5x Reorder the terms: (4 + x)(-7 + x) = 5x Multiply (4 + x) * (-7 + x) (4(-7 + x) + x(-7 + x)) = 5x ((-7 * 4 + x * 4) + x(-7 + x)) = 5x ((-28 + 4x) + x(-7 + x)) = 5x (-28 + 4x + (-7 * x + x * x)) = 5x (-28 + 4x + (-7x + x2)) = 5x Combine like terms: 4x + -7x = -3x (-28 + -3x + x2) = 5x Solving -28 + -3x + x2 = 5x Solving for variable 'x'. Reorder the terms: -28 + -3x + -5x + x2 = 5x + -5x Combine like terms: -3x + -5x = -8x -28 + -8x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -28 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -8x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -8x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -8x + x2 = 0 + 28 -8x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -8x + x2 = 28 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 = 28 + 16 Reorder the terms: 16 + -8x + x2 = 28 + 16 Combine like terms: 28 + 16 = 44 16 + -8x + x2 = 44 Factor a perfect square on the left side: (x + -4)(x + -4) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (x + -4) equal to 6.633249581 and -6.633249581.Subproblem 1
x + -4 = 6.633249581 Simplifying x + -4 = 6.633249581 Reorder the terms: -4 + x = 6.633249581 Solving -4 + x = 6.633249581 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 = 6.633249581 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6.633249581 + 4 x = 6.633249581 + 4 Combine like terms: 6.633249581 + 4 = 10.633249581 x = 10.633249581 Simplifying x = 10.633249581Subproblem 2
x + -4 = -6.633249581 Simplifying x + -4 = -6.633249581 Reorder the terms: -4 + x = -6.633249581 Solving -4 + x = -6.633249581 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 = -6.633249581 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6.633249581 + 4 x = -6.633249581 + 4 Combine like terms: -6.633249581 + 4 = -2.633249581 x = -2.633249581 Simplifying x = -2.633249581Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.633249581, -2.633249581}
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