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Simplifying (x)(x + 20) = 3000 Reorder the terms: x(20 + x) = 3000 (20 * x + x * x) = 3000 (20x + x2) = 3000 Solving 20x + x2 = 3000 Solving for variable 'x'. Reorder the terms: -3000 + 20x + x2 = 3000 + -3000 Combine like terms: 3000 + -3000 = 0 -3000 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3000' to each side of the equation. -3000 + 20x + 3000 + x2 = 0 + 3000 Reorder the terms: -3000 + 3000 + 20x + x2 = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + 20x + x2 = 0 + 3000 20x + x2 = 0 + 3000 Combine like terms: 0 + 3000 = 3000 20x + x2 = 3000 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 3000 + 100 Reorder the terms: 100 + 20x + x2 = 3000 + 100 Combine like terms: 3000 + 100 = 3100 100 + 20x + x2 = 3100 Factor a perfect square on the left side: (x + 10)(x + 10) = 3100 Calculate the square root of the right side: 55.677643628 Break this problem into two subproblems by setting (x + 10) equal to 55.677643628 and -55.677643628.Subproblem 1
x + 10 = 55.677643628 Simplifying x + 10 = 55.677643628 Reorder the terms: 10 + x = 55.677643628 Solving 10 + x = 55.677643628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 55.677643628 + -10 Combine like terms: 10 + -10 = 0 0 + x = 55.677643628 + -10 x = 55.677643628 + -10 Combine like terms: 55.677643628 + -10 = 45.677643628 x = 45.677643628 Simplifying x = 45.677643628Subproblem 2
x + 10 = -55.677643628 Simplifying x + 10 = -55.677643628 Reorder the terms: 10 + x = -55.677643628 Solving 10 + x = -55.677643628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -55.677643628 + -10 Combine like terms: 10 + -10 = 0 0 + x = -55.677643628 + -10 x = -55.677643628 + -10 Combine like terms: -55.677643628 + -10 = -65.677643628 x = -65.677643628 Simplifying x = -65.677643628Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.677643628, -65.677643628}
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