# 2a² + 4a + 5 = 0

kuCAu 2021-03-05 Answered
$2a²+4a+5=0$
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## Expert Answer

coffentw
Answered 2021-03-06 Author has 103 answers

We are given: $2a²+4a+5=0$
Solve by completing the square. First, we write the equation in the form $x²+bx=c$. Subtract 5 from both sides: $2a²+4a=-5$
Divide both sides by 2: $a²+2a=-\left(\frac{5}{2}\right)$
Complete the square by adding ${\left(\frac{b}{2}\right)}^{2}$ on both sides. Here, b=2 so we add ${\left(\frac{2}{2}\right)}^{2}=1$ to both sides.
$a²+2a+1=-\left(\frac{5}{2}\right)+1$
$\left(a+1\right)²=-\left(\frac{3}{2}\right)$
Take the square root of both sides: $a+1=±\sqrt{-\frac{3}{2}}$
The square root of a negative number is not defined so the equation has no real solution.

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Jeffrey Jordon
Answered 2021-08-10 Author has 2027 answers

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