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

## Step-by-step Solution

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###  Videos

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

##  Step-by-step Solution 

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

Multiply both sides of the equation by $-1$

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

Break the equation in $2$ factors and set each equal to zero, to obtain

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

Solve the equation ($1$)

$x-2=0$
9

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

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

Canceling terms on both sides

$x=2$
11

Solve the equation ($2$)

$x-5=0$
12

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

$x-5+5=0+5$
13

Canceling terms on both sides

$x=5$
14

Combining all solutions, the $2$ solutions of the equation are

$x=2,\:x=5$

$x=2,\:x=5$

##  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

Solve for xFind the rootsSolve by factoringSolve by completing the squareSolve by quadratic formula (general formula)Find break even pointsFind the discriminant

SnapXam A2

### beta Got a different answer? Verify it!

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0
a
b
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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

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