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Simplifying x2 + 19x + -83 = 0 Reorder the terms: -83 + 19x + x2 = 0 Solving -83 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '83' to each side of the equation. -83 + 19x + 83 + x2 = 0 + 83 Reorder the terms: -83 + 83 + 19x + x2 = 0 + 83 Combine like terms: -83 + 83 = 0 0 + 19x + x2 = 0 + 83 19x + x2 = 0 + 83 Combine like terms: 0 + 83 = 83 19x + x2 = 83 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = 83 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 83 + 90.25 Combine like terms: 83 + 90.25 = 173.25 90.25 + 19x + x2 = 173.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 173.25 Calculate the square root of the right side: 13.162446581 Break this problem into two subproblems by setting (x + 9.5) equal to 13.162446581 and -13.162446581.Subproblem 1
x + 9.5 = 13.162446581 Simplifying x + 9.5 = 13.162446581 Reorder the terms: 9.5 + x = 13.162446581 Solving 9.5 + x = 13.162446581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 13.162446581 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 13.162446581 + -9.5 x = 13.162446581 + -9.5 Combine like terms: 13.162446581 + -9.5 = 3.662446581 x = 3.662446581 Simplifying x = 3.662446581Subproblem 2
x + 9.5 = -13.162446581 Simplifying x + 9.5 = -13.162446581 Reorder the terms: 9.5 + x = -13.162446581 Solving 9.5 + x = -13.162446581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -13.162446581 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -13.162446581 + -9.5 x = -13.162446581 + -9.5 Combine like terms: -13.162446581 + -9.5 = -22.662446581 x = -22.662446581 Simplifying x = -22.662446581Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.662446581, -22.662446581}
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