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# Solve the quadratic equation $2x^2+2x+1=0$

## Step-by-step Solution

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$x=\frac{-2+2i}{4},\:x=\frac{-2-2i}{4}$
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##  Step-by-step Solution 

Problem to solve:

$2x^2+2x+1=0$

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To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where in this case $a=2$, $b=2$ and $c=1$. Then substitute the values of the coefficients of the equation in the quadratic formula: $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-2\pm \sqrt{2^2-4\cdot 2\cdot 1}}{2\cdot 2}$

Learn how to solve quadratic equations problems step by step online.

$x=\frac{-2\pm \sqrt{2^2-4\cdot 2\cdot 1}}{2\cdot 2}$

Learn how to solve quadratic equations problems step by step online. Solve the quadratic equation 2x^2+2x+1=0. To find the roots of a polynomial of the form ax^2+bx+c we use the quadratic formula, where in this case a=2, b=2 and c=1. Then substitute the values of the coefficients of the equation in the quadratic formula: \displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}. Simplify \frac{-2\pm \sqrt{2^2-4\cdot 2\cdot 1}}{2\cdot 2}. To obtain the two solutions, divide the equation in two equations, one when \pm is positive (+), and another when \pm is negative (-). Calculate the power \sqrt{-4} using complex numbers.

$x=\frac{-2+2i}{4},\:x=\frac{-2-2i}{4}$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve for xFind the rootsSolve by factoringSolve by completing the squareSolve by quadratic formulaFind break even points

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e
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ln
log
log
lim
d/dx
Dx
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>=
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sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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