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Simplifying (2x + -7)(x + 1) = 1 Reorder the terms: (-7 + 2x)(x + 1) = 1 Reorder the terms: (-7 + 2x)(1 + x) = 1 Multiply (-7 + 2x) * (1 + x) (-7(1 + x) + 2x * (1 + x)) = 1 ((1 * -7 + x * -7) + 2x * (1 + x)) = 1 ((-7 + -7x) + 2x * (1 + x)) = 1 (-7 + -7x + (1 * 2x + x * 2x)) = 1 (-7 + -7x + (2x + 2x2)) = 1 Combine like terms: -7x + 2x = -5x (-7 + -5x + 2x2) = 1 Solving -7 + -5x + 2x2 = 1 Solving for variable 'x'. Reorder the terms: -7 + -1 + -5x + 2x2 = 1 + -1 Combine like terms: -7 + -1 = -8 -8 + -5x + 2x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -8 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + -2.5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -2.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -2.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2.5x + x2 = 0 + 4 -2.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2.5x + x2 = 4 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 4 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 4 + 1.5625 Combine like terms: 4 + 1.5625 = 5.5625 1.5625 + -2.5x + x2 = 5.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (x + -1.25) equal to 2.358495283 and -2.358495283.Subproblem 1
x + -1.25 = 2.358495283 Simplifying x + -1.25 = 2.358495283 Reorder the terms: -1.25 + x = 2.358495283 Solving -1.25 + x = 2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.358495283 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.358495283 + 1.25 x = 2.358495283 + 1.25 Combine like terms: 2.358495283 + 1.25 = 3.608495283 x = 3.608495283 Simplifying x = 3.608495283Subproblem 2
x + -1.25 = -2.358495283 Simplifying x + -1.25 = -2.358495283 Reorder the terms: -1.25 + x = -2.358495283 Solving -1.25 + x = -2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.358495283 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.358495283 + 1.25 x = -2.358495283 + 1.25 Combine like terms: -2.358495283 + 1.25 = -1.108495283 x = -1.108495283 Simplifying x = -1.108495283Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.608495283, -1.108495283}
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