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Simplifying (2x + -1)(x + 3) = 13 Reorder the terms: (-1 + 2x)(x + 3) = 13 Reorder the terms: (-1 + 2x)(3 + x) = 13 Multiply (-1 + 2x) * (3 + x) (-1(3 + x) + 2x * (3 + x)) = 13 ((3 * -1 + x * -1) + 2x * (3 + x)) = 13 ((-3 + -1x) + 2x * (3 + x)) = 13 (-3 + -1x + (3 * 2x + x * 2x)) = 13 (-3 + -1x + (6x + 2x2)) = 13 Combine like terms: -1x + 6x = 5x (-3 + 5x + 2x2) = 13 Solving -3 + 5x + 2x2 = 13 Solving for variable 'x'. Reorder the terms: -3 + -13 + 5x + 2x2 = 13 + -13 Combine like terms: -3 + -13 = -16 -16 + 5x + 2x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -16 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8 + 2.5x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 2.5x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 2.5x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 2.5x + x2 = 0 + 8 2.5x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 2.5x + x2 = 8 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 = 8 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 8 + 1.5625 Combine like terms: 8 + 1.5625 = 9.5625 1.5625 + 2.5x + x2 = 9.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (x + 1.25) equal to 3.092329219 and -3.092329219.Subproblem 1
x + 1.25 = 3.092329219 Simplifying x + 1.25 = 3.092329219 Reorder the terms: 1.25 + x = 3.092329219 Solving 1.25 + x = 3.092329219 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 = 3.092329219 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 3.092329219 + -1.25 x = 3.092329219 + -1.25 Combine like terms: 3.092329219 + -1.25 = 1.842329219 x = 1.842329219 Simplifying x = 1.842329219Subproblem 2
x + 1.25 = -3.092329219 Simplifying x + 1.25 = -3.092329219 Reorder the terms: 1.25 + x = -3.092329219 Solving 1.25 + x = -3.092329219 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 = -3.092329219 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -3.092329219 + -1.25 x = -3.092329219 + -1.25 Combine like terms: -3.092329219 + -1.25 = -4.342329219 x = -4.342329219 Simplifying x = -4.342329219Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.842329219, -4.342329219}
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