Step-by-step Solution

Solve the quadratic equation $-x^2+7x-10=0$

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asin
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sinh
cosh
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coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Final Answer

$x=5,\:x=2$
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Step-by-step Solution

Problem to solve:

$-x^2+7x-10=0$

Solving method

1

For a simpler handling of the equation, change the sign of all terms, multiplying the entire whole by $-1$

$x^2-7x+10=0$
2

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where in this case $a=1$, $b=-7$ and $c=10$. Then substitute the values of the coefficients of the equation in the quadratic formula:

  • $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{7\pm 3}{2}$
3

To obtain the two solutions, divide the equation in two equations, one when $\pm$ is positive ($+$), and another when $\pm$ is negative ($-$)

$x=\frac{7+3}{2},\:x=\frac{7-3}{2}$
4

Subtract the values $7$ and $-3$

$x=\frac{7+3}{2},\:x=\frac{4}{2}$
5

Add the values $7$ and $3$

$x=\frac{10}{2},\:x=\frac{4}{2}$
6

Divide $10$ by $2$

$x=5,\:x=\frac{4}{2}$
7

Divide $4$ by $2$

$x=5,\:x=2$

Final Answer

$x=5,\:x=2$
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7
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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

Tips on how to improve your answer:

$-x^2+7x-10=0$

Main topic:

Quadratic equations

Related Formulas:

1. See formulas

Time to solve it:

~ 0.45 s