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# Solve the quadratic equation $\frac{1}{4}x^2-3x-2=0$

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##  Final answer to the problem

$x=\left(3+\sqrt{11}\right)\cdot 2,\:x=\left(3-\sqrt{11}\right)\cdot 2$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Solve for x
• Find the derivative using the definition
• Solve by quadratic formula (general formula)
• Simplify
• Find the integral
• Find the derivative
• Factor
• Factor by completing the square
• Find the roots
Can't find a method? Tell us so we can add it.
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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 $a=\frac{1}{4}$, $b=-3$ and $c=-2$. Then substitute the values of the coefficients of the equation in the quadratic formula: $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{3\pm \sqrt{{\left(-3\right)}^2-4\cdot \left(\frac{1}{4}\right)\cdot -2}}{2\cdot \left(\frac{1}{4}\right)}$

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

$x=\frac{3\pm \sqrt{{\left(-3\right)}^2-4\cdot \left(\frac{1}{4}\right)\cdot -2}}{2\cdot \left(\frac{1}{4}\right)}$

Learn how to solve quadratic equations problems step by step online. Solve the quadratic equation 1/4x^2-3x+-2=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=\frac{1}{4}, b=-3 and c=-2. Then substitute the values of the coefficients of the equation in the quadratic formula: \displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}. Simplifying. To obtain the two solutions, divide the equation in two equations, one when \pm is positive (+), and another when \pm is negative (-). Divide fractions \frac{3+\sqrt{11}}{\frac{1}{2}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}.

##  Final answer to the problem

$x=\left(3+\sqrt{11}\right)\cdot 2,\:x=\left(3-\sqrt{11}\right)\cdot 2$

##  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

SnapXam A2

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a
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v
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x
y
z
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(◻)
+
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×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

###  Main Topic: Quadratic Equations

The quadratic equations (or second degree equations) are those equations where the greatest exponent to which the unknown is raised is the exponent 2.