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Simplifying (3x + 2)(x + 4) + -1(2x + 1)(2x + -1) = 0 Reorder the terms: (2 + 3x)(x + 4) + -1(2x + 1)(2x + -1) = 0 Reorder the terms: (2 + 3x)(4 + x) + -1(2x + 1)(2x + -1) = 0 Multiply (2 + 3x) * (4 + x) (2(4 + x) + 3x * (4 + x)) + -1(2x + 1)(2x + -1) = 0 ((4 * 2 + x * 2) + 3x * (4 + x)) + -1(2x + 1)(2x + -1) = 0 ((8 + 2x) + 3x * (4 + x)) + -1(2x + 1)(2x + -1) = 0 (8 + 2x + (4 * 3x + x * 3x)) + -1(2x + 1)(2x + -1) = 0 (8 + 2x + (12x + 3x2)) + -1(2x + 1)(2x + -1) = 0 Combine like terms: 2x + 12x = 14x (8 + 14x + 3x2) + -1(2x + 1)(2x + -1) = 0 Reorder the terms: 8 + 14x + 3x2 + -1(1 + 2x)(2x + -1) = 0 Reorder the terms: 8 + 14x + 3x2 + -1(1 + 2x)(-1 + 2x) = 0 Multiply (1 + 2x) * (-1 + 2x) 8 + 14x + 3x2 + -1(1(-1 + 2x) + 2x * (-1 + 2x)) = 0 8 + 14x + 3x2 + -1((-1 * 1 + 2x * 1) + 2x * (-1 + 2x)) = 0 8 + 14x + 3x2 + -1((-1 + 2x) + 2x * (-1 + 2x)) = 0 8 + 14x + 3x2 + -1(-1 + 2x + (-1 * 2x + 2x * 2x)) = 0 8 + 14x + 3x2 + -1(-1 + 2x + (-2x + 4x2)) = 0 Combine like terms: 2x + -2x = 0 8 + 14x + 3x2 + -1(-1 + 0 + 4x2) = 0 8 + 14x + 3x2 + -1(-1 + 4x2) = 0 8 + 14x + 3x2 + (-1 * -1 + 4x2 * -1) = 0 8 + 14x + 3x2 + (1 + -4x2) = 0 Reorder the terms: 8 + 1 + 14x + 3x2 + -4x2 = 0 Combine like terms: 8 + 1 = 9 9 + 14x + 3x2 + -4x2 = 0 Combine like terms: 3x2 + -4x2 = -1x2 9 + 14x + -1x2 = 0 Solving 9 + 14x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + -14x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -14x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -14x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -14x + x2 = 0 + 9 -14x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -14x + x2 = 9 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 9 + 49 Reorder the terms: 49 + -14x + x2 = 9 + 49 Combine like terms: 9 + 49 = 58 49 + -14x + x2 = 58 Factor a perfect square on the left side: (x + -7)(x + -7) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (x + -7) equal to 7.615773106 and -7.615773106.Subproblem 1
x + -7 = 7.615773106 Simplifying x + -7 = 7.615773106 Reorder the terms: -7 + x = 7.615773106 Solving -7 + x = 7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 7.615773106 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.615773106 + 7 x = 7.615773106 + 7 Combine like terms: 7.615773106 + 7 = 14.615773106 x = 14.615773106 Simplifying x = 14.615773106Subproblem 2
x + -7 = -7.615773106 Simplifying x + -7 = -7.615773106 Reorder the terms: -7 + x = -7.615773106 Solving -7 + x = -7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -7.615773106 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.615773106 + 7 x = -7.615773106 + 7 Combine like terms: -7.615773106 + 7 = -0.615773106 x = -0.615773106 Simplifying x = -0.615773106Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.615773106, -0.615773106}
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