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Simplifying (7 + -1x)(x + 2) = 4 Reorder the terms: (7 + -1x)(2 + x) = 4 Multiply (7 + -1x) * (2 + x) (7(2 + x) + -1x * (2 + x)) = 4 ((2 * 7 + x * 7) + -1x * (2 + x)) = 4 ((14 + 7x) + -1x * (2 + x)) = 4 (14 + 7x + (2 * -1x + x * -1x)) = 4 (14 + 7x + (-2x + -1x2)) = 4 Combine like terms: 7x + -2x = 5x (14 + 5x + -1x2) = 4 Solving 14 + 5x + -1x2 = 4 Solving for variable 'x'. Reorder the terms: 14 + -4 + 5x + -1x2 = 4 + -4 Combine like terms: 14 + -4 = 10 10 + 5x + -1x2 = 4 + -4 Combine like terms: 4 + -4 = 0 10 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -5x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -5x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -5x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -5x + x2 = 0 + 10 -5x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -5x + x2 = 10 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 10 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 10 + 6.25 Combine like terms: 10 + 6.25 = 16.25 6.25 + -5x + x2 = 16.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + -2.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + -2.5 = 4.031128874 Simplifying x + -2.5 = 4.031128874 Reorder the terms: -2.5 + x = 4.031128874 Solving -2.5 + x = 4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 4.031128874 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.031128874 + 2.5 x = 4.031128874 + 2.5 Combine like terms: 4.031128874 + 2.5 = 6.531128874 x = 6.531128874 Simplifying x = 6.531128874Subproblem 2
x + -2.5 = -4.031128874 Simplifying x + -2.5 = -4.031128874 Reorder the terms: -2.5 + x = -4.031128874 Solving -2.5 + x = -4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -4.031128874 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.031128874 + 2.5 x = -4.031128874 + 2.5 Combine like terms: -4.031128874 + 2.5 = -1.531128874 x = -1.531128874 Simplifying x = -1.531128874Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.531128874, -1.531128874}
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