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

Step-by-step Solution

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asinh
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Final Answer

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

Problem to solve:

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

Specify the solving method

1

Factor the trinomial by $-1$ for an easier handling

$-\left(x^2-7x+10\right)=0$
2

Factor the trinomial $-\left(x^2-7x+10\right)$ finding two numbers that multiply to form $10$ and added form $-7$

$\begin{matrix}\left(-2\right)\left(-5\right)=10\\ \left(-2\right)+\left(-5\right)=-7\end{matrix}$
3

Thus

$-\left(x^2-7x+10\right)=0$
4

Factor the trinomial $\left(x^2-7x+10\right)$ finding two numbers that multiply to form $10$ and added form $-7$

$\begin{matrix}\left(-2\right)\left(-5\right)=10\\ \left(-2\right)+\left(-5\right)=-7\end{matrix}$
5

Thus

$-\left(x-2\right)\left(x-5\right)=0$
6

Solve the product $-(x-2)$

$\left(-x+2\right)\left(x-5\right)=0$
7

Break the equation in factors and set each equal to zero, to obtain

$x-5=0,\:-x+2=0$
8

Solve the equation ($1$)

$x-5=0$
9

We need to isolate the dependent variable $x$, we can do that by subtracting $-5$ from both sides of the equation

$x=5$
10

Solve the equation ($2$)

$-x+2=0$
11

We need to isolate the dependent variable $x$, we can do that by subtracting $2$ from both sides of the equation

$-x=-2$
12

Multiply both sides of the equation by $-1$

$x=2$
13

The $2$ solutions of the equation are

$x=5,\:x=2$

Final Answer

$x=5,\:x=2$
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Got another answer? Verify it!

Go!
1
2
3
4
5
6
7
8
9
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

Time to solve it:

~ 0.05 s