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Simplifying (x + 3)(4x + 5) = 4 Reorder the terms: (3 + x)(4x + 5) = 4 Reorder the terms: (3 + x)(5 + 4x) = 4 Multiply (3 + x) * (5 + 4x) (3(5 + 4x) + x(5 + 4x)) = 4 ((5 * 3 + 4x * 3) + x(5 + 4x)) = 4 ((15 + 12x) + x(5 + 4x)) = 4 (15 + 12x + (5 * x + 4x * x)) = 4 (15 + 12x + (5x + 4x2)) = 4 Combine like terms: 12x + 5x = 17x (15 + 17x + 4x2) = 4 Solving 15 + 17x + 4x2 = 4 Solving for variable 'x'. Reorder the terms: 15 + -4 + 17x + 4x2 = 4 + -4 Combine like terms: 15 + -4 = 11 11 + 17x + 4x2 = 4 + -4 Combine like terms: 4 + -4 = 0 11 + 17x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.75 + 4.25x + x2 = 0 Move the constant term to the right: Add '-2.75' to each side of the equation. 2.75 + 4.25x + -2.75 + x2 = 0 + -2.75 Reorder the terms: 2.75 + -2.75 + 4.25x + x2 = 0 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + 4.25x + x2 = 0 + -2.75 4.25x + x2 = 0 + -2.75 Combine like terms: 0 + -2.75 = -2.75 4.25x + x2 = -2.75 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = -2.75 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = -2.75 + 4.515625 Combine like terms: -2.75 + 4.515625 = 1.765625 4.515625 + 4.25x + x2 = 1.765625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (x + 2.125) equal to 1.328768227 and -1.328768227.Subproblem 1
x + 2.125 = 1.328768227 Simplifying x + 2.125 = 1.328768227 Reorder the terms: 2.125 + x = 1.328768227 Solving 2.125 + x = 1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 1.328768227 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 1.328768227 + -2.125 x = 1.328768227 + -2.125 Combine like terms: 1.328768227 + -2.125 = -0.796231773 x = -0.796231773 Simplifying x = -0.796231773Subproblem 2
x + 2.125 = -1.328768227 Simplifying x + 2.125 = -1.328768227 Reorder the terms: 2.125 + x = -1.328768227 Solving 2.125 + x = -1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -1.328768227 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -1.328768227 + -2.125 x = -1.328768227 + -2.125 Combine like terms: -1.328768227 + -2.125 = -3.453768227 x = -3.453768227 Simplifying x = -3.453768227Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.796231773, -3.453768227}
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