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Simplifying x2 + 20x + -203 = 0 Reorder the terms: -203 + 20x + x2 = 0 Solving -203 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '203' to each side of the equation. -203 + 20x + 203 + x2 = 0 + 203 Reorder the terms: -203 + 203 + 20x + x2 = 0 + 203 Combine like terms: -203 + 203 = 0 0 + 20x + x2 = 0 + 203 20x + x2 = 0 + 203 Combine like terms: 0 + 203 = 203 20x + x2 = 203 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 = 203 + 100 Reorder the terms: 100 + 20x + x2 = 203 + 100 Combine like terms: 203 + 100 = 303 100 + 20x + x2 = 303 Factor a perfect square on the left side: (x + 10)(x + 10) = 303 Calculate the square root of the right side: 17.406895186 Break this problem into two subproblems by setting (x + 10) equal to 17.406895186 and -17.406895186.Subproblem 1
x + 10 = 17.406895186 Simplifying x + 10 = 17.406895186 Reorder the terms: 10 + x = 17.406895186 Solving 10 + x = 17.406895186 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 = 17.406895186 + -10 Combine like terms: 10 + -10 = 0 0 + x = 17.406895186 + -10 x = 17.406895186 + -10 Combine like terms: 17.406895186 + -10 = 7.406895186 x = 7.406895186 Simplifying x = 7.406895186Subproblem 2
x + 10 = -17.406895186 Simplifying x + 10 = -17.406895186 Reorder the terms: 10 + x = -17.406895186 Solving 10 + x = -17.406895186 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 = -17.406895186 + -10 Combine like terms: 10 + -10 = 0 0 + x = -17.406895186 + -10 x = -17.406895186 + -10 Combine like terms: -17.406895186 + -10 = -27.406895186 x = -27.406895186 Simplifying x = -27.406895186Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.406895186, -27.406895186}
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