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Simplifying x2 + -38x + 80 = 0 Reorder the terms: 80 + -38x + x2 = 0 Solving 80 + -38x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + -38x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + -38x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -38x + x2 = 0 + -80 -38x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 -38x + x2 = -80 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 = -80 + 361 Reorder the terms: 361 + -38x + x2 = -80 + 361 Combine like terms: -80 + 361 = 281 361 + -38x + x2 = 281 Factor a perfect square on the left side: (x + -19)(x + -19) = 281 Calculate the square root of the right side: 16.763054614 Break this problem into two subproblems by setting (x + -19) equal to 16.763054614 and -16.763054614.Subproblem 1
x + -19 = 16.763054614 Simplifying x + -19 = 16.763054614 Reorder the terms: -19 + x = 16.763054614 Solving -19 + x = 16.763054614 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 = 16.763054614 + 19 Combine like terms: -19 + 19 = 0 0 + x = 16.763054614 + 19 x = 16.763054614 + 19 Combine like terms: 16.763054614 + 19 = 35.763054614 x = 35.763054614 Simplifying x = 35.763054614Subproblem 2
x + -19 = -16.763054614 Simplifying x + -19 = -16.763054614 Reorder the terms: -19 + x = -16.763054614 Solving -19 + x = -16.763054614 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 = -16.763054614 + 19 Combine like terms: -19 + 19 = 0 0 + x = -16.763054614 + 19 x = -16.763054614 + 19 Combine like terms: -16.763054614 + 19 = 2.236945386 x = 2.236945386 Simplifying x = 2.236945386Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.763054614, 2.236945386}
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