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Simplifying x(x + -7) = 2(x + x + -7) Reorder the terms: x(-7 + x) = 2(x + x + -7) (-7 * x + x * x) = 2(x + x + -7) (-7x + x2) = 2(x + x + -7) Reorder the terms: -7x + x2 = 2(-7 + x + x) Combine like terms: x + x = 2x -7x + x2 = 2(-7 + 2x) -7x + x2 = (-7 * 2 + 2x * 2) -7x + x2 = (-14 + 4x) Solving -7x + x2 = -14 + 4x Solving for variable 'x'. Reorder the terms: 14 + -7x + -4x + x2 = -14 + 4x + 14 + -4x Combine like terms: -7x + -4x = -11x 14 + -11x + x2 = -14 + 4x + 14 + -4x Reorder the terms: 14 + -11x + x2 = -14 + 14 + 4x + -4x Combine like terms: -14 + 14 = 0 14 + -11x + x2 = 0 + 4x + -4x 14 + -11x + x2 = 4x + -4x Combine like terms: 4x + -4x = 0 14 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -11x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -11x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -11x + x2 = 0 + -14 -11x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -11x + x2 = -14 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -14 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -14 + 30.25 Combine like terms: -14 + 30.25 = 16.25 30.25 + -11x + x2 = 16.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + -5.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + -5.5 = 4.031128874 Simplifying x + -5.5 = 4.031128874 Reorder the terms: -5.5 + x = 4.031128874 Solving -5.5 + x = 4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 4.031128874 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 4.031128874 + 5.5 x = 4.031128874 + 5.5 Combine like terms: 4.031128874 + 5.5 = 9.531128874 x = 9.531128874 Simplifying x = 9.531128874Subproblem 2
x + -5.5 = -4.031128874 Simplifying x + -5.5 = -4.031128874 Reorder the terms: -5.5 + x = -4.031128874 Solving -5.5 + x = -4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -4.031128874 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -4.031128874 + 5.5 x = -4.031128874 + 5.5 Combine like terms: -4.031128874 + 5.5 = 1.468871126 x = 1.468871126 Simplifying x = 1.468871126Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.531128874, 1.468871126}
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