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Simplifying (2x + 1)(x + -7) = 5 Reorder the terms: (1 + 2x)(x + -7) = 5 Reorder the terms: (1 + 2x)(-7 + x) = 5 Multiply (1 + 2x) * (-7 + x) (1(-7 + x) + 2x * (-7 + x)) = 5 ((-7 * 1 + x * 1) + 2x * (-7 + x)) = 5 ((-7 + 1x) + 2x * (-7 + x)) = 5 (-7 + 1x + (-7 * 2x + x * 2x)) = 5 (-7 + 1x + (-14x + 2x2)) = 5 Combine like terms: 1x + -14x = -13x (-7 + -13x + 2x2) = 5 Solving -7 + -13x + 2x2 = 5 Solving for variable 'x'. Reorder the terms: -7 + -5 + -13x + 2x2 = 5 + -5 Combine like terms: -7 + -5 = -12 -12 + -13x + 2x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -12 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + -6.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -6.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -6.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -6.5x + x2 = 0 + 6 -6.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -6.5x + x2 = 6 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 6 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 6 + 10.5625 Combine like terms: 6 + 10.5625 = 16.5625 10.5625 + -6.5x + x2 = 16.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 16.5625 Calculate the square root of the right side: 4.069705149 Break this problem into two subproblems by setting (x + -3.25) equal to 4.069705149 and -4.069705149.Subproblem 1
x + -3.25 = 4.069705149 Simplifying x + -3.25 = 4.069705149 Reorder the terms: -3.25 + x = 4.069705149 Solving -3.25 + x = 4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 4.069705149 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 4.069705149 + 3.25 x = 4.069705149 + 3.25 Combine like terms: 4.069705149 + 3.25 = 7.319705149 x = 7.319705149 Simplifying x = 7.319705149Subproblem 2
x + -3.25 = -4.069705149 Simplifying x + -3.25 = -4.069705149 Reorder the terms: -3.25 + x = -4.069705149 Solving -3.25 + x = -4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -4.069705149 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -4.069705149 + 3.25 x = -4.069705149 + 3.25 Combine like terms: -4.069705149 + 3.25 = -0.819705149 x = -0.819705149 Simplifying x = -0.819705149Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.319705149, -0.819705149}
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