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Simplifying (4x + 3)(x + 2) = (3x)(2x + 2) Reorder the terms: (3 + 4x)(x + 2) = (3x)(2x + 2) Reorder the terms: (3 + 4x)(2 + x) = (3x)(2x + 2) Multiply (3 + 4x) * (2 + x) (3(2 + x) + 4x * (2 + x)) = (3x)(2x + 2) ((2 * 3 + x * 3) + 4x * (2 + x)) = (3x)(2x + 2) ((6 + 3x) + 4x * (2 + x)) = (3x)(2x + 2) (6 + 3x + (2 * 4x + x * 4x)) = (3x)(2x + 2) (6 + 3x + (8x + 4x2)) = (3x)(2x + 2) Combine like terms: 3x + 8x = 11x (6 + 11x + 4x2) = (3x)(2x + 2) Remove parenthesis around (3x) 6 + 11x + 4x2 = 3x(2x + 2) Reorder the terms: 6 + 11x + 4x2 = 3x(2 + 2x) 6 + 11x + 4x2 = (2 * 3x + 2x * 3x) 6 + 11x + 4x2 = (6x + 6x2) Solving 6 + 11x + 4x2 = 6x + 6x2 Solving for variable 'x'. Reorder the terms: 6 + 11x + -6x + 4x2 + -6x2 = 6x + 6x2 + -6x + -6x2 Combine like terms: 11x + -6x = 5x 6 + 5x + 4x2 + -6x2 = 6x + 6x2 + -6x + -6x2 Combine like terms: 4x2 + -6x2 = -2x2 6 + 5x + -2x2 = 6x + 6x2 + -6x + -6x2 Reorder the terms: 6 + 5x + -2x2 = 6x + -6x + 6x2 + -6x2 Combine like terms: 6x + -6x = 0 6 + 5x + -2x2 = 0 + 6x2 + -6x2 6 + 5x + -2x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 6 + 5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -3 + -2.5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -2.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -2.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2.5x + x2 = 0 + 3 -2.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -2.5x + x2 = 3 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 = 3 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 3 + 1.5625 Combine like terms: 3 + 1.5625 = 4.5625 1.5625 + -2.5x + x2 = 4.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (x + -1.25) equal to 2.136000936 and -2.136000936.Subproblem 1
x + -1.25 = 2.136000936 Simplifying x + -1.25 = 2.136000936 Reorder the terms: -1.25 + x = 2.136000936 Solving -1.25 + x = 2.136000936 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 = 2.136000936 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.136000936 + 1.25 x = 2.136000936 + 1.25 Combine like terms: 2.136000936 + 1.25 = 3.386000936 x = 3.386000936 Simplifying x = 3.386000936Subproblem 2
x + -1.25 = -2.136000936 Simplifying x + -1.25 = -2.136000936 Reorder the terms: -1.25 + x = -2.136000936 Solving -1.25 + x = -2.136000936 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 = -2.136000936 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.136000936 + 1.25 x = -2.136000936 + 1.25 Combine like terms: -2.136000936 + 1.25 = -0.886000936 x = -0.886000936 Simplifying x = -0.886000936Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.386000936, -0.886000936}
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