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Simplifying x2 + 20x + -2300 = 0 Reorder the terms: -2300 + 20x + x2 = 0 Solving -2300 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2300' to each side of the equation. -2300 + 20x + 2300 + x2 = 0 + 2300 Reorder the terms: -2300 + 2300 + 20x + x2 = 0 + 2300 Combine like terms: -2300 + 2300 = 0 0 + 20x + x2 = 0 + 2300 20x + x2 = 0 + 2300 Combine like terms: 0 + 2300 = 2300 20x + x2 = 2300 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 = 2300 + 100 Reorder the terms: 100 + 20x + x2 = 2300 + 100 Combine like terms: 2300 + 100 = 2400 100 + 20x + x2 = 2400 Factor a perfect square on the left side: (x + 10)(x + 10) = 2400 Calculate the square root of the right side: 48.989794856 Break this problem into two subproblems by setting (x + 10) equal to 48.989794856 and -48.989794856.Subproblem 1
x + 10 = 48.989794856 Simplifying x + 10 = 48.989794856 Reorder the terms: 10 + x = 48.989794856 Solving 10 + x = 48.989794856 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 = 48.989794856 + -10 Combine like terms: 10 + -10 = 0 0 + x = 48.989794856 + -10 x = 48.989794856 + -10 Combine like terms: 48.989794856 + -10 = 38.989794856 x = 38.989794856 Simplifying x = 38.989794856Subproblem 2
x + 10 = -48.989794856 Simplifying x + 10 = -48.989794856 Reorder the terms: 10 + x = -48.989794856 Solving 10 + x = -48.989794856 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 = -48.989794856 + -10 Combine like terms: 10 + -10 = 0 0 + x = -48.989794856 + -10 x = -48.989794856 + -10 Combine like terms: -48.989794856 + -10 = -58.989794856 x = -58.989794856 Simplifying x = -58.989794856Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.989794856, -58.989794856}
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