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Solve the quadratic equation $10x^2-x+51=0$

Step-by-step Solution

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Final answer to the problem

$x=\frac{1+45.1552876i}{20},\:x=\frac{1-45.1552876i}{20}$
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Step-by-step Solution

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  • Solve for x
  • Find the derivative using the definition
  • Solve by quadratic formula (general formula)
  • Simplify
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  • Find the derivative
  • Factor
  • Factor by completing the square
  • Find the roots
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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 $a=10$, $b=-1$ and $c=51$. Then substitute the values of the coefficients of the equation in the quadratic formula: $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-1\cdot -1\pm \sqrt{{\left(-1\right)}^2-4\cdot 10\cdot 51}}{2\cdot 10}$

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$x=\frac{-1\cdot -1\pm \sqrt{{\left(-1\right)}^2-4\cdot 10\cdot 51}}{2\cdot 10}$

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Learn how to solve problems step by step online. Solve the quadratic equation 10x^2-x+51=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=10, b=-1 and c=51. 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 (-). Calculate the power \sqrt{-2039} using complex numbers.

Final answer to the problem

$x=\frac{1+45.1552876i}{20},\:x=\frac{1-45.1552876i}{20}$

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Function Plot

Plotting: $10x^2-x+51$

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

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