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Simplifying (0.25x + 3)(x) = 160 Reorder the terms: (3 + 0.25x)(x) = 160 Reorder the terms for easier multiplication: x(3 + 0.25x) = 160 (3 * x + 0.25x * x) = 160 (3x + 0.25x2) = 160 Solving 3x + 0.25x2 = 160 Solving for variable 'x'. Reorder the terms: -160 + 3x + 0.25x2 = 160 + -160 Combine like terms: 160 + -160 = 0 -160 + 3x + 0.25x2 = 0 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -640 + 12x + x2 = 0 Move the constant term to the right: Add '640' to each side of the equation. -640 + 12x + 640 + x2 = 0 + 640 Reorder the terms: -640 + 640 + 12x + x2 = 0 + 640 Combine like terms: -640 + 640 = 0 0 + 12x + x2 = 0 + 640 12x + x2 = 0 + 640 Combine like terms: 0 + 640 = 640 12x + x2 = 640 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 640 + 36 Reorder the terms: 36 + 12x + x2 = 640 + 36 Combine like terms: 640 + 36 = 676 36 + 12x + x2 = 676 Factor a perfect square on the left side: (x + 6)(x + 6) = 676 Calculate the square root of the right side: 26 Break this problem into two subproblems by setting (x + 6) equal to 26 and -26.Subproblem 1
x + 6 = 26 Simplifying x + 6 = 26 Reorder the terms: 6 + x = 26 Solving 6 + x = 26 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 26 + -6 Combine like terms: 6 + -6 = 0 0 + x = 26 + -6 x = 26 + -6 Combine like terms: 26 + -6 = 20 x = 20 Simplifying x = 20Subproblem 2
x + 6 = -26 Simplifying x + 6 = -26 Reorder the terms: 6 + x = -26 Solving 6 + x = -26 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -26 + -6 Combine like terms: 6 + -6 = 0 0 + x = -26 + -6 x = -26 + -6 Combine like terms: -26 + -6 = -32 x = -32 Simplifying x = -32Solution
The solution to the problem is based on the solutions from the subproblems. x = {20, -32}
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