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Simplifying x2 + 38x + -84 = 0 Reorder the terms: -84 + 38x + x2 = 0 Solving -84 + 38x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + 38x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + 38x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 38x + x2 = 0 + 84 38x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 38x + x2 = 84 The x term is 38x. Take half its coefficient (19). Square it (361) and add it to both sides. Add '361' to each side of the equation. 38x + 361 + x2 = 84 + 361 Reorder the terms: 361 + 38x + x2 = 84 + 361 Combine like terms: 84 + 361 = 445 361 + 38x + x2 = 445 Factor a perfect square on the left side: (x + 19)(x + 19) = 445 Calculate the square root of the right side: 21.09502311 Break this problem into two subproblems by setting (x + 19) equal to 21.09502311 and -21.09502311.Subproblem 1
x + 19 = 21.09502311 Simplifying x + 19 = 21.09502311 Reorder the terms: 19 + x = 21.09502311 Solving 19 + x = 21.09502311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = 21.09502311 + -19 Combine like terms: 19 + -19 = 0 0 + x = 21.09502311 + -19 x = 21.09502311 + -19 Combine like terms: 21.09502311 + -19 = 2.09502311 x = 2.09502311 Simplifying x = 2.09502311Subproblem 2
x + 19 = -21.09502311 Simplifying x + 19 = -21.09502311 Reorder the terms: 19 + x = -21.09502311 Solving 19 + x = -21.09502311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = -21.09502311 + -19 Combine like terms: 19 + -19 = 0 0 + x = -21.09502311 + -19 x = -21.09502311 + -19 Combine like terms: -21.09502311 + -19 = -40.09502311 x = -40.09502311 Simplifying x = -40.09502311Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.09502311, -40.09502311}
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