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Simplifying (7 + -3x)(x + 4) = 18 Reorder the terms: (7 + -3x)(4 + x) = 18 Multiply (7 + -3x) * (4 + x) (7(4 + x) + -3x * (4 + x)) = 18 ((4 * 7 + x * 7) + -3x * (4 + x)) = 18 ((28 + 7x) + -3x * (4 + x)) = 18 (28 + 7x + (4 * -3x + x * -3x)) = 18 (28 + 7x + (-12x + -3x2)) = 18 Combine like terms: 7x + -12x = -5x (28 + -5x + -3x2) = 18 Solving 28 + -5x + -3x2 = 18 Solving for variable 'x'. Reorder the terms: 28 + -18 + -5x + -3x2 = 18 + -18 Combine like terms: 28 + -18 = 10 10 + -5x + -3x2 = 18 + -18 Combine like terms: 18 + -18 = 0 10 + -5x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -3.333333333 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 1.666666667x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 1.666666667x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + 3.333333333 1.666666667x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 1.666666667x + x2 = 3.333333333 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 3.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 3.333333333 + 0.6944444447 Combine like terms: 3.333333333 + 0.6944444447 = 4.0277777777 0.6944444447 + 1.666666667x + x2 = 4.0277777777 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 4.0277777777 Calculate the square root of the right side: 2.00693243 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 2.00693243 and -2.00693243.Subproblem 1
x + 0.8333333335 = 2.00693243 Simplifying x + 0.8333333335 = 2.00693243 Reorder the terms: 0.8333333335 + x = 2.00693243 Solving 0.8333333335 + x = 2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 2.00693243 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 2.00693243 + -0.8333333335 x = 2.00693243 + -0.8333333335 Combine like terms: 2.00693243 + -0.8333333335 = 1.1735990965 x = 1.1735990965 Simplifying x = 1.1735990965Subproblem 2
x + 0.8333333335 = -2.00693243 Simplifying x + 0.8333333335 = -2.00693243 Reorder the terms: 0.8333333335 + x = -2.00693243 Solving 0.8333333335 + x = -2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -2.00693243 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -2.00693243 + -0.8333333335 x = -2.00693243 + -0.8333333335 Combine like terms: -2.00693243 + -0.8333333335 = -2.8402657635 x = -2.8402657635 Simplifying x = -2.8402657635Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1735990965, -2.8402657635}
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