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Simplifying x2 + 20x + -91 = 0 Reorder the terms: -91 + 20x + x2 = 0 Solving -91 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '91' to each side of the equation. -91 + 20x + 91 + x2 = 0 + 91 Reorder the terms: -91 + 91 + 20x + x2 = 0 + 91 Combine like terms: -91 + 91 = 0 0 + 20x + x2 = 0 + 91 20x + x2 = 0 + 91 Combine like terms: 0 + 91 = 91 20x + x2 = 91 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 = 91 + 100 Reorder the terms: 100 + 20x + x2 = 91 + 100 Combine like terms: 91 + 100 = 191 100 + 20x + x2 = 191 Factor a perfect square on the left side: (x + 10)(x + 10) = 191 Calculate the square root of the right side: 13.820274961 Break this problem into two subproblems by setting (x + 10) equal to 13.820274961 and -13.820274961.Subproblem 1
x + 10 = 13.820274961 Simplifying x + 10 = 13.820274961 Reorder the terms: 10 + x = 13.820274961 Solving 10 + x = 13.820274961 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 = 13.820274961 + -10 Combine like terms: 10 + -10 = 0 0 + x = 13.820274961 + -10 x = 13.820274961 + -10 Combine like terms: 13.820274961 + -10 = 3.820274961 x = 3.820274961 Simplifying x = 3.820274961Subproblem 2
x + 10 = -13.820274961 Simplifying x + 10 = -13.820274961 Reorder the terms: 10 + x = -13.820274961 Solving 10 + x = -13.820274961 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 = -13.820274961 + -10 Combine like terms: 10 + -10 = 0 0 + x = -13.820274961 + -10 x = -13.820274961 + -10 Combine like terms: -13.820274961 + -10 = -23.820274961 x = -23.820274961 Simplifying x = -23.820274961Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.820274961, -23.820274961}
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