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Simplifying (x + 7)(5x + 2) = 28 Reorder the terms: (7 + x)(5x + 2) = 28 Reorder the terms: (7 + x)(2 + 5x) = 28 Multiply (7 + x) * (2 + 5x) (7(2 + 5x) + x(2 + 5x)) = 28 ((2 * 7 + 5x * 7) + x(2 + 5x)) = 28 ((14 + 35x) + x(2 + 5x)) = 28 (14 + 35x + (2 * x + 5x * x)) = 28 (14 + 35x + (2x + 5x2)) = 28 Combine like terms: 35x + 2x = 37x (14 + 37x + 5x2) = 28 Solving 14 + 37x + 5x2 = 28 Solving for variable 'x'. Reorder the terms: 14 + -28 + 37x + 5x2 = 28 + -28 Combine like terms: 14 + -28 = -14 -14 + 37x + 5x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -14 + 37x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + 7.4x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + 7.4x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + 7.4x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + 7.4x + x2 = 0 + 2.8 7.4x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 7.4x + x2 = 2.8 The x term is 7.4x. Take half its coefficient (3.7). Square it (13.69) and add it to both sides. Add '13.69' to each side of the equation. 7.4x + 13.69 + x2 = 2.8 + 13.69 Reorder the terms: 13.69 + 7.4x + x2 = 2.8 + 13.69 Combine like terms: 2.8 + 13.69 = 16.49 13.69 + 7.4x + x2 = 16.49 Factor a perfect square on the left side: (x + 3.7)(x + 3.7) = 16.49 Calculate the square root of the right side: 4.060788101 Break this problem into two subproblems by setting (x + 3.7) equal to 4.060788101 and -4.060788101.Subproblem 1
x + 3.7 = 4.060788101 Simplifying x + 3.7 = 4.060788101 Reorder the terms: 3.7 + x = 4.060788101 Solving 3.7 + x = 4.060788101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.7' to each side of the equation. 3.7 + -3.7 + x = 4.060788101 + -3.7 Combine like terms: 3.7 + -3.7 = 0.0 0.0 + x = 4.060788101 + -3.7 x = 4.060788101 + -3.7 Combine like terms: 4.060788101 + -3.7 = 0.360788101 x = 0.360788101 Simplifying x = 0.360788101Subproblem 2
x + 3.7 = -4.060788101 Simplifying x + 3.7 = -4.060788101 Reorder the terms: 3.7 + x = -4.060788101 Solving 3.7 + x = -4.060788101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.7' to each side of the equation. 3.7 + -3.7 + x = -4.060788101 + -3.7 Combine like terms: 3.7 + -3.7 = 0.0 0.0 + x = -4.060788101 + -3.7 x = -4.060788101 + -3.7 Combine like terms: -4.060788101 + -3.7 = -7.760788101 x = -7.760788101 Simplifying x = -7.760788101Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.360788101, -7.760788101}
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