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Simplifying x + (x + 28)(2x + -38) = 652 Reorder the terms: x + (28 + x)(2x + -38) = 652 Reorder the terms: x + (28 + x)(-38 + 2x) = 652 Multiply (28 + x) * (-38 + 2x) x + (28(-38 + 2x) + x(-38 + 2x)) = 652 x + ((-38 * 28 + 2x * 28) + x(-38 + 2x)) = 652 x + ((-1064 + 56x) + x(-38 + 2x)) = 652 x + (-1064 + 56x + (-38 * x + 2x * x)) = 652 x + (-1064 + 56x + (-38x + 2x2)) = 652 Combine like terms: 56x + -38x = 18x x + (-1064 + 18x + 2x2) = 652 Reorder the terms: -1064 + x + 18x + 2x2 = 652 Combine like terms: x + 18x = 19x -1064 + 19x + 2x2 = 652 Solving -1064 + 19x + 2x2 = 652 Solving for variable 'x'. Reorder the terms: -1064 + -652 + 19x + 2x2 = 652 + -652 Combine like terms: -1064 + -652 = -1716 -1716 + 19x + 2x2 = 652 + -652 Combine like terms: 652 + -652 = 0 -1716 + 19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -858 + 9.5x + x2 = 0 Move the constant term to the right: Add '858' to each side of the equation. -858 + 9.5x + 858 + x2 = 0 + 858 Reorder the terms: -858 + 858 + 9.5x + x2 = 0 + 858 Combine like terms: -858 + 858 = 0 0 + 9.5x + x2 = 0 + 858 9.5x + x2 = 0 + 858 Combine like terms: 0 + 858 = 858 9.5x + x2 = 858 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = 858 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 858 + 22.5625 Combine like terms: 858 + 22.5625 = 880.5625 22.5625 + 9.5x + x2 = 880.5625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 880.5625 Calculate the square root of the right side: 29.674273369 Break this problem into two subproblems by setting (x + 4.75) equal to 29.674273369 and -29.674273369.Subproblem 1
x + 4.75 = 29.674273369 Simplifying x + 4.75 = 29.674273369 Reorder the terms: 4.75 + x = 29.674273369 Solving 4.75 + x = 29.674273369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 29.674273369 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 29.674273369 + -4.75 x = 29.674273369 + -4.75 Combine like terms: 29.674273369 + -4.75 = 24.924273369 x = 24.924273369 Simplifying x = 24.924273369Subproblem 2
x + 4.75 = -29.674273369 Simplifying x + 4.75 = -29.674273369 Reorder the terms: 4.75 + x = -29.674273369 Solving 4.75 + x = -29.674273369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -29.674273369 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -29.674273369 + -4.75 x = -29.674273369 + -4.75 Combine like terms: -29.674273369 + -4.75 = -34.424273369 x = -34.424273369 Simplifying x = -34.424273369Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.924273369, -34.424273369}
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