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Solve the quadratic equation $x^2-3x+5=8$

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Solution

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Final Answer

$x=\frac{3+\sqrt{21}}{2},\:x=\frac{3-\sqrt{21}}{2}$
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Step-by-step Solution

Problem to solve:

$x^2-3x+5=8$

Specify the solving method

1

Group the terms of the equation by moving the terms that have the variable $x$ to the left side, and those that do not have it to the right side

$x^2-3x=8-5$

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$x^2-3x=8-5$

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Learn how to solve quadratic equations problems step by step online. Solve the quadratic equation x^2-3x+5=8. Group the terms of the equation by moving the terms that have the variable x to the left side, and those that do not have it to the right side. Subtract the values 8 and -5. Rewrite the equation. To find the roots of a polynomial of the form ax^2+bx+c we use the quadratic formula, where in this case a=1, b=-3 and c=-3. Then substitute the values of the coefficients of the equation in the quadratic formula: \displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.

Final Answer

$x=\frac{3+\sqrt{21}}{2},\:x=\frac{3-\sqrt{21}}{2}$

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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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0
a
b
c
d
f
g
m
n
u
v
w
x
y
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.
(◻)
+
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×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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

How to improve your answer:

Similar Problems Solved

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$x^2-8x-1008=0$

Main topic:

Quadratic equations

Used formulas:

1. See formulas

Time to solve it:

~ 0.1 s

Related topics:

Quadratic equationsEquationsQuadratic Formula

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