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Simplifying (8 + x)(x + 38) = 225 Reorder the terms: (8 + x)(38 + x) = 225 Multiply (8 + x) * (38 + x) (8(38 + x) + x(38 + x)) = 225 ((38 * 8 + x * 8) + x(38 + x)) = 225 ((304 + 8x) + x(38 + x)) = 225 (304 + 8x + (38 * x + x * x)) = 225 (304 + 8x + (38x + x2)) = 225 Combine like terms: 8x + 38x = 46x (304 + 46x + x2) = 225 Solving 304 + 46x + x2 = 225 Solving for variable 'x'. Reorder the terms: 304 + -225 + 46x + x2 = 225 + -225 Combine like terms: 304 + -225 = 79 79 + 46x + x2 = 225 + -225 Combine like terms: 225 + -225 = 0 79 + 46x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-79' to each side of the equation. 79 + 46x + -79 + x2 = 0 + -79 Reorder the terms: 79 + -79 + 46x + x2 = 0 + -79 Combine like terms: 79 + -79 = 0 0 + 46x + x2 = 0 + -79 46x + x2 = 0 + -79 Combine like terms: 0 + -79 = -79 46x + x2 = -79 The x term is 46x. Take half its coefficient (23). Square it (529) and add it to both sides. Add '529' to each side of the equation. 46x + 529 + x2 = -79 + 529 Reorder the terms: 529 + 46x + x2 = -79 + 529 Combine like terms: -79 + 529 = 450 529 + 46x + x2 = 450 Factor a perfect square on the left side: (x + 23)(x + 23) = 450 Calculate the square root of the right side: 21.213203436 Break this problem into two subproblems by setting (x + 23) equal to 21.213203436 and -21.213203436.Subproblem 1
x + 23 = 21.213203436 Simplifying x + 23 = 21.213203436 Reorder the terms: 23 + x = 21.213203436 Solving 23 + x = 21.213203436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = 21.213203436 + -23 Combine like terms: 23 + -23 = 0 0 + x = 21.213203436 + -23 x = 21.213203436 + -23 Combine like terms: 21.213203436 + -23 = -1.786796564 x = -1.786796564 Simplifying x = -1.786796564Subproblem 2
x + 23 = -21.213203436 Simplifying x + 23 = -21.213203436 Reorder the terms: 23 + x = -21.213203436 Solving 23 + x = -21.213203436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = -21.213203436 + -23 Combine like terms: 23 + -23 = 0 0 + x = -21.213203436 + -23 x = -21.213203436 + -23 Combine like terms: -21.213203436 + -23 = -44.213203436 x = -44.213203436 Simplifying x = -44.213203436Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.786796564, -44.213203436}
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