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Simplifying (2x + 1)(x + 4) + 13 = 2x + -10x Reorder the terms: (1 + 2x)(x + 4) + 13 = 2x + -10x Reorder the terms: (1 + 2x)(4 + x) + 13 = 2x + -10x Multiply (1 + 2x) * (4 + x) (1(4 + x) + 2x * (4 + x)) + 13 = 2x + -10x ((4 * 1 + x * 1) + 2x * (4 + x)) + 13 = 2x + -10x ((4 + 1x) + 2x * (4 + x)) + 13 = 2x + -10x (4 + 1x + (4 * 2x + x * 2x)) + 13 = 2x + -10x (4 + 1x + (8x + 2x2)) + 13 = 2x + -10x Combine like terms: 1x + 8x = 9x (4 + 9x + 2x2) + 13 = 2x + -10x Reorder the terms: 4 + 13 + 9x + 2x2 = 2x + -10x Combine like terms: 4 + 13 = 17 17 + 9x + 2x2 = 2x + -10x Combine like terms: 2x + -10x = -8x 17 + 9x + 2x2 = -8x Solving 17 + 9x + 2x2 = -8x Solving for variable 'x'. Reorder the terms: 17 + 9x + 8x + 2x2 = -8x + 8x Combine like terms: 9x + 8x = 17x 17 + 17x + 2x2 = -8x + 8x Combine like terms: -8x + 8x = 0 17 + 17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + 8.5x + x2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + 8.5x + -8.5 + x2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + 8.5x + x2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + 8.5x + x2 = 0 + -8.5 8.5x + x2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 8.5x + x2 = -8.5 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = -8.5 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = -8.5 + 18.0625 Combine like terms: -8.5 + 18.0625 = 9.5625 18.0625 + 8.5x + x2 = 9.5625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (x + 4.25) equal to 3.092329219 and -3.092329219.Subproblem 1
x + 4.25 = 3.092329219 Simplifying x + 4.25 = 3.092329219 Reorder the terms: 4.25 + x = 3.092329219 Solving 4.25 + x = 3.092329219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 3.092329219 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 3.092329219 + -4.25 x = 3.092329219 + -4.25 Combine like terms: 3.092329219 + -4.25 = -1.157670781 x = -1.157670781 Simplifying x = -1.157670781Subproblem 2
x + 4.25 = -3.092329219 Simplifying x + 4.25 = -3.092329219 Reorder the terms: 4.25 + x = -3.092329219 Solving 4.25 + x = -3.092329219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -3.092329219 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -3.092329219 + -4.25 x = -3.092329219 + -4.25 Combine like terms: -3.092329219 + -4.25 = -7.342329219 x = -7.342329219 Simplifying x = -7.342329219Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.157670781, -7.342329219}
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