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

Step-by-step Solution

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Solution

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Final Answer

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

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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 , 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 , 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

$x=2,\:x=5$

Final Answer

$x=2,\:x=5$

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 quadratic formula (general formula)Find break even pointsFind the discriminant

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Function Plot

Plotting: $-x^2+7x-10$

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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
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:

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Main Topic: Quadratic Equations

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

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