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Simplifying x2 + 38x + -100 = 0 Reorder the terms: -100 + 38x + x2 = 0 Solving -100 + 38x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 38x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 38x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 38x + x2 = 0 + 100 38x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 38x + x2 = 100 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 = 100 + 361 Reorder the terms: 361 + 38x + x2 = 100 + 361 Combine like terms: 100 + 361 = 461 361 + 38x + x2 = 461 Factor a perfect square on the left side: (x + 19)(x + 19) = 461 Calculate the square root of the right side: 21.470910554 Break this problem into two subproblems by setting (x + 19) equal to 21.470910554 and -21.470910554.Subproblem 1
x + 19 = 21.470910554 Simplifying x + 19 = 21.470910554 Reorder the terms: 19 + x = 21.470910554 Solving 19 + x = 21.470910554 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 = 21.470910554 + -19 Combine like terms: 19 + -19 = 0 0 + x = 21.470910554 + -19 x = 21.470910554 + -19 Combine like terms: 21.470910554 + -19 = 2.470910554 x = 2.470910554 Simplifying x = 2.470910554Subproblem 2
x + 19 = -21.470910554 Simplifying x + 19 = -21.470910554 Reorder the terms: 19 + x = -21.470910554 Solving 19 + x = -21.470910554 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 = -21.470910554 + -19 Combine like terms: 19 + -19 = 0 0 + x = -21.470910554 + -19 x = -21.470910554 + -19 Combine like terms: -21.470910554 + -19 = -40.470910554 x = -40.470910554 Simplifying x = -40.470910554Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.470910554, -40.470910554}
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