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Simplifying (7x + -12)(x + 4) = 9 Reorder the terms: (-12 + 7x)(x + 4) = 9 Reorder the terms: (-12 + 7x)(4 + x) = 9 Multiply (-12 + 7x) * (4 + x) (-12(4 + x) + 7x * (4 + x)) = 9 ((4 * -12 + x * -12) + 7x * (4 + x)) = 9 ((-48 + -12x) + 7x * (4 + x)) = 9 (-48 + -12x + (4 * 7x + x * 7x)) = 9 (-48 + -12x + (28x + 7x2)) = 9 Combine like terms: -12x + 28x = 16x (-48 + 16x + 7x2) = 9 Solving -48 + 16x + 7x2 = 9 Solving for variable 'x'. Reorder the terms: -48 + -9 + 16x + 7x2 = 9 + -9 Combine like terms: -48 + -9 = -57 -57 + 16x + 7x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -57 + 16x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -8.142857143 + 2.285714286x + x2 = 0 Move the constant term to the right: Add '8.142857143' to each side of the equation. -8.142857143 + 2.285714286x + 8.142857143 + x2 = 0 + 8.142857143 Reorder the terms: -8.142857143 + 8.142857143 + 2.285714286x + x2 = 0 + 8.142857143 Combine like terms: -8.142857143 + 8.142857143 = 0.000000000 0.000000000 + 2.285714286x + x2 = 0 + 8.142857143 2.285714286x + x2 = 0 + 8.142857143 Combine like terms: 0 + 8.142857143 = 8.142857143 2.285714286x + x2 = 8.142857143 The x term is 2.285714286x. Take half its coefficient (1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. 2.285714286x + 1.306122449 + x2 = 8.142857143 + 1.306122449 Reorder the terms: 1.306122449 + 2.285714286x + x2 = 8.142857143 + 1.306122449 Combine like terms: 8.142857143 + 1.306122449 = 9.448979592 1.306122449 + 2.285714286x + x2 = 9.448979592 Factor a perfect square on the left side: (x + 1.142857143)(x + 1.142857143) = 9.448979592 Calculate the square root of the right side: 3.073919256 Break this problem into two subproblems by setting (x + 1.142857143) equal to 3.073919256 and -3.073919256.Subproblem 1
x + 1.142857143 = 3.073919256 Simplifying x + 1.142857143 = 3.073919256 Reorder the terms: 1.142857143 + x = 3.073919256 Solving 1.142857143 + x = 3.073919256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.142857143' to each side of the equation. 1.142857143 + -1.142857143 + x = 3.073919256 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + x = 3.073919256 + -1.142857143 x = 3.073919256 + -1.142857143 Combine like terms: 3.073919256 + -1.142857143 = 1.931062113 x = 1.931062113 Simplifying x = 1.931062113Subproblem 2
x + 1.142857143 = -3.073919256 Simplifying x + 1.142857143 = -3.073919256 Reorder the terms: 1.142857143 + x = -3.073919256 Solving 1.142857143 + x = -3.073919256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.142857143' to each side of the equation. 1.142857143 + -1.142857143 + x = -3.073919256 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + x = -3.073919256 + -1.142857143 x = -3.073919256 + -1.142857143 Combine like terms: -3.073919256 + -1.142857143 = -4.216776399 x = -4.216776399 Simplifying x = -4.216776399Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.931062113, -4.216776399}
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