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Simplifying (x + 4)(x + -6) = 7x Reorder the terms: (4 + x)(x + -6) = 7x Reorder the terms: (4 + x)(-6 + x) = 7x Multiply (4 + x) * (-6 + x) (4(-6 + x) + x(-6 + x)) = 7x ((-6 * 4 + x * 4) + x(-6 + x)) = 7x ((-24 + 4x) + x(-6 + x)) = 7x (-24 + 4x + (-6 * x + x * x)) = 7x (-24 + 4x + (-6x + x2)) = 7x Combine like terms: 4x + -6x = -2x (-24 + -2x + x2) = 7x Solving -24 + -2x + x2 = 7x Solving for variable 'x'. Reorder the terms: -24 + -2x + -7x + x2 = 7x + -7x Combine like terms: -2x + -7x = -9x -24 + -9x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -24 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -9x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -9x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -9x + x2 = 0 + 24 -9x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -9x + x2 = 24 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 24 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 24 + 20.25 Combine like terms: 24 + 20.25 = 44.25 20.25 + -9x + x2 = 44.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (x + -4.5) equal to 6.652067348 and -6.652067348.Subproblem 1
x + -4.5 = 6.652067348 Simplifying x + -4.5 = 6.652067348 Reorder the terms: -4.5 + x = 6.652067348 Solving -4.5 + x = 6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 6.652067348 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 6.652067348 + 4.5 x = 6.652067348 + 4.5 Combine like terms: 6.652067348 + 4.5 = 11.152067348 x = 11.152067348 Simplifying x = 11.152067348Subproblem 2
x + -4.5 = -6.652067348 Simplifying x + -4.5 = -6.652067348 Reorder the terms: -4.5 + x = -6.652067348 Solving -4.5 + x = -6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -6.652067348 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -6.652067348 + 4.5 x = -6.652067348 + 4.5 Combine like terms: -6.652067348 + 4.5 = -2.152067348 x = -2.152067348 Simplifying x = -2.152067348Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.152067348, -2.152067348}
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