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Simplifying x2 + 20x + -194 = 0 Reorder the terms: -194 + 20x + x2 = 0 Solving -194 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '194' to each side of the equation. -194 + 20x + 194 + x2 = 0 + 194 Reorder the terms: -194 + 194 + 20x + x2 = 0 + 194 Combine like terms: -194 + 194 = 0 0 + 20x + x2 = 0 + 194 20x + x2 = 0 + 194 Combine like terms: 0 + 194 = 194 20x + x2 = 194 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 = 194 + 100 Reorder the terms: 100 + 20x + x2 = 194 + 100 Combine like terms: 194 + 100 = 294 100 + 20x + x2 = 294 Factor a perfect square on the left side: (x + 10)(x + 10) = 294 Calculate the square root of the right side: 17.146428199 Break this problem into two subproblems by setting (x + 10) equal to 17.146428199 and -17.146428199.Subproblem 1
x + 10 = 17.146428199 Simplifying x + 10 = 17.146428199 Reorder the terms: 10 + x = 17.146428199 Solving 10 + x = 17.146428199 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 = 17.146428199 + -10 Combine like terms: 10 + -10 = 0 0 + x = 17.146428199 + -10 x = 17.146428199 + -10 Combine like terms: 17.146428199 + -10 = 7.146428199 x = 7.146428199 Simplifying x = 7.146428199Subproblem 2
x + 10 = -17.146428199 Simplifying x + 10 = -17.146428199 Reorder the terms: 10 + x = -17.146428199 Solving 10 + x = -17.146428199 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 = -17.146428199 + -10 Combine like terms: 10 + -10 = 0 0 + x = -17.146428199 + -10 x = -17.146428199 + -10 Combine like terms: -17.146428199 + -10 = -27.146428199 x = -27.146428199 Simplifying x = -27.146428199Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.146428199, -27.146428199}
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