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Simplifying x2 + 20x + -300 = 550 Reorder the terms: -300 + 20x + x2 = 550 Solving -300 + 20x + x2 = 550 Solving for variable 'x'. Reorder the terms: -300 + -550 + 20x + x2 = 550 + -550 Combine like terms: -300 + -550 = -850 -850 + 20x + x2 = 550 + -550 Combine like terms: 550 + -550 = 0 -850 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '850' to each side of the equation. -850 + 20x + 850 + x2 = 0 + 850 Reorder the terms: -850 + 850 + 20x + x2 = 0 + 850 Combine like terms: -850 + 850 = 0 0 + 20x + x2 = 0 + 850 20x + x2 = 0 + 850 Combine like terms: 0 + 850 = 850 20x + x2 = 850 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 = 850 + 100 Reorder the terms: 100 + 20x + x2 = 850 + 100 Combine like terms: 850 + 100 = 950 100 + 20x + x2 = 950 Factor a perfect square on the left side: (x + 10)(x + 10) = 950 Calculate the square root of the right side: 30.822070015 Break this problem into two subproblems by setting (x + 10) equal to 30.822070015 and -30.822070015.Subproblem 1
x + 10 = 30.822070015 Simplifying x + 10 = 30.822070015 Reorder the terms: 10 + x = 30.822070015 Solving 10 + x = 30.822070015 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 = 30.822070015 + -10 Combine like terms: 10 + -10 = 0 0 + x = 30.822070015 + -10 x = 30.822070015 + -10 Combine like terms: 30.822070015 + -10 = 20.822070015 x = 20.822070015 Simplifying x = 20.822070015Subproblem 2
x + 10 = -30.822070015 Simplifying x + 10 = -30.822070015 Reorder the terms: 10 + x = -30.822070015 Solving 10 + x = -30.822070015 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 = -30.822070015 + -10 Combine like terms: 10 + -10 = 0 0 + x = -30.822070015 + -10 x = -30.822070015 + -10 Combine like terms: -30.822070015 + -10 = -40.822070015 x = -40.822070015 Simplifying x = -40.822070015Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.822070015, -40.822070015}
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