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Simplifying 44 = (2x + 1)(x + 3) Reorder the terms: 44 = (1 + 2x)(x + 3) Reorder the terms: 44 = (1 + 2x)(3 + x) Multiply (1 + 2x) * (3 + x) 44 = (1(3 + x) + 2x * (3 + x)) 44 = ((3 * 1 + x * 1) + 2x * (3 + x)) 44 = ((3 + 1x) + 2x * (3 + x)) 44 = (3 + 1x + (3 * 2x + x * 2x)) 44 = (3 + 1x + (6x + 2x2)) Combine like terms: 1x + 6x = 7x 44 = (3 + 7x + 2x2) Solving 44 = 3 + 7x + 2x2 Solving for variable 'x'. Combine like terms: 44 + -3 = 41 41 + -7x + -2x2 = 3 + 7x + 2x2 + -3 + -7x + -2x2 Reorder the terms: 41 + -7x + -2x2 = 3 + -3 + 7x + -7x + 2x2 + -2x2 Combine like terms: 3 + -3 = 0 41 + -7x + -2x2 = 0 + 7x + -7x + 2x2 + -2x2 41 + -7x + -2x2 = 7x + -7x + 2x2 + -2x2 Combine like terms: 7x + -7x = 0 41 + -7x + -2x2 = 0 + 2x2 + -2x2 41 + -7x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 41 + -7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -20.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '20.5' to each side of the equation. -20.5 + 3.5x + 20.5 + x2 = 0 + 20.5 Reorder the terms: -20.5 + 20.5 + 3.5x + x2 = 0 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + 3.5x + x2 = 0 + 20.5 3.5x + x2 = 0 + 20.5 Combine like terms: 0 + 20.5 = 20.5 3.5x + x2 = 20.5 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 20.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 20.5 + 3.0625 Combine like terms: 20.5 + 3.0625 = 23.5625 3.0625 + 3.5x + x2 = 23.5625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 23.5625 Calculate the square root of the right side: 4.85412196 Break this problem into two subproblems by setting (x + 1.75) equal to 4.85412196 and -4.85412196.Subproblem 1
x + 1.75 = 4.85412196 Simplifying x + 1.75 = 4.85412196 Reorder the terms: 1.75 + x = 4.85412196 Solving 1.75 + x = 4.85412196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 4.85412196 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 4.85412196 + -1.75 x = 4.85412196 + -1.75 Combine like terms: 4.85412196 + -1.75 = 3.10412196 x = 3.10412196 Simplifying x = 3.10412196Subproblem 2
x + 1.75 = -4.85412196 Simplifying x + 1.75 = -4.85412196 Reorder the terms: 1.75 + x = -4.85412196 Solving 1.75 + x = -4.85412196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -4.85412196 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -4.85412196 + -1.75 x = -4.85412196 + -1.75 Combine like terms: -4.85412196 + -1.75 = -6.60412196 x = -6.60412196 Simplifying x = -6.60412196Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.10412196, -6.60412196}
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