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Simplifying x2 + 20x + 17 = 83 Reorder the terms: 17 + 20x + x2 = 83 Solving 17 + 20x + x2 = 83 Solving for variable 'x'. Reorder the terms: 17 + -83 + 20x + x2 = 83 + -83 Combine like terms: 17 + -83 = -66 -66 + 20x + x2 = 83 + -83 Combine like terms: 83 + -83 = 0 -66 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + 20x + 66 + x2 = 0 + 66 Reorder the terms: -66 + 66 + 20x + x2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + 20x + x2 = 0 + 66 20x + x2 = 0 + 66 Combine like terms: 0 + 66 = 66 20x + x2 = 66 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 = 66 + 100 Reorder the terms: 100 + 20x + x2 = 66 + 100 Combine like terms: 66 + 100 = 166 100 + 20x + x2 = 166 Factor a perfect square on the left side: (x + 10)(x + 10) = 166 Calculate the square root of the right side: 12.884098727 Break this problem into two subproblems by setting (x + 10) equal to 12.884098727 and -12.884098727.Subproblem 1
x + 10 = 12.884098727 Simplifying x + 10 = 12.884098727 Reorder the terms: 10 + x = 12.884098727 Solving 10 + x = 12.884098727 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 = 12.884098727 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.884098727 + -10 x = 12.884098727 + -10 Combine like terms: 12.884098727 + -10 = 2.884098727 x = 2.884098727 Simplifying x = 2.884098727Subproblem 2
x + 10 = -12.884098727 Simplifying x + 10 = -12.884098727 Reorder the terms: 10 + x = -12.884098727 Solving 10 + x = -12.884098727 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 = -12.884098727 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.884098727 + -10 x = -12.884098727 + -10 Combine like terms: -12.884098727 + -10 = -22.884098727 x = -22.884098727 Simplifying x = -22.884098727Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.884098727, -22.884098727}
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