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Simplifying ((x + 7) + 3)((4x + 3) + 2) = 110 Reorder the terms: ((7 + x) + 3)((4x + 3) + 2) = 110 Remove parenthesis around (7 + x) (7 + x + 3)((4x + 3) + 2) = 110 Reorder the terms: (7 + 3 + x)((4x + 3) + 2) = 110 Combine like terms: 7 + 3 = 10 (10 + x)((4x + 3) + 2) = 110 Reorder the terms: (10 + x)((3 + 4x) + 2) = 110 Remove parenthesis around (3 + 4x) (10 + x)(3 + 4x + 2) = 110 Reorder the terms: (10 + x)(3 + 2 + 4x) = 110 Combine like terms: 3 + 2 = 5 (10 + x)(5 + 4x) = 110 Multiply (10 + x) * (5 + 4x) (10(5 + 4x) + x(5 + 4x)) = 110 ((5 * 10 + 4x * 10) + x(5 + 4x)) = 110 ((50 + 40x) + x(5 + 4x)) = 110 (50 + 40x + (5 * x + 4x * x)) = 110 (50 + 40x + (5x + 4x2)) = 110 Combine like terms: 40x + 5x = 45x (50 + 45x + 4x2) = 110 Solving 50 + 45x + 4x2 = 110 Solving for variable 'x'. Reorder the terms: 50 + -110 + 45x + 4x2 = 110 + -110 Combine like terms: 50 + -110 = -60 -60 + 45x + 4x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -60 + 45x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -15 + 11.25x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 11.25x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 11.25x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 11.25x + x2 = 0 + 15 11.25x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 11.25x + x2 = 15 The x term is 11.25x. Take half its coefficient (5.625). Square it (31.640625) and add it to both sides. Add '31.640625' to each side of the equation. 11.25x + 31.640625 + x2 = 15 + 31.640625 Reorder the terms: 31.640625 + 11.25x + x2 = 15 + 31.640625 Combine like terms: 15 + 31.640625 = 46.640625 31.640625 + 11.25x + x2 = 46.640625 Factor a perfect square on the left side: (x + 5.625)(x + 5.625) = 46.640625 Calculate the square root of the right side: 6.82939419 Break this problem into two subproblems by setting (x + 5.625) equal to 6.82939419 and -6.82939419.Subproblem 1
x + 5.625 = 6.82939419 Simplifying x + 5.625 = 6.82939419 Reorder the terms: 5.625 + x = 6.82939419 Solving 5.625 + x = 6.82939419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.625' to each side of the equation. 5.625 + -5.625 + x = 6.82939419 + -5.625 Combine like terms: 5.625 + -5.625 = 0.000 0.000 + x = 6.82939419 + -5.625 x = 6.82939419 + -5.625 Combine like terms: 6.82939419 + -5.625 = 1.20439419 x = 1.20439419 Simplifying x = 1.20439419Subproblem 2
x + 5.625 = -6.82939419 Simplifying x + 5.625 = -6.82939419 Reorder the terms: 5.625 + x = -6.82939419 Solving 5.625 + x = -6.82939419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.625' to each side of the equation. 5.625 + -5.625 + x = -6.82939419 + -5.625 Combine like terms: 5.625 + -5.625 = 0.000 0.000 + x = -6.82939419 + -5.625 x = -6.82939419 + -5.625 Combine like terms: -6.82939419 + -5.625 = -12.45439419 x = -12.45439419 Simplifying x = -12.45439419Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.20439419, -12.45439419}
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