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Explicação passo-a-passo:
Solve for x over the real numbers:
2 x^2 + 5 x + 1 = 0
Divide both sides by 2:
x^2 + (5 x)/2 + 1/2 = 0
Subtract 1/2 from both sides:
x^2 + (5 x)/2 = -1/2
Add 25/16 to both sides:
x^2 + (5 x)/2 + 25/16 = 17/16
Write the left hand side as a square:
(x + 5/4)^2 = 17/16
Take the square root of both sides:
x + 5/4 = sqrt(17)/4 or x + 5/4 = -sqrt(17)/4
Subtract 5/4 from both sides:
x = sqrt(17)/4 - 5/4 or x + 5/4 = -sqrt(17)/4
Subtract 5/4 from both sides:
Answer: |
| x = sqrt(17)/4 - 5/4
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