# I need help on this equation: x(x+4)=21

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Another way to solve quadratic equations is to use the quadratic formula. Any equation of the form ax² + bx + c = 0 can be solved for x by the formula:

x = (-b² - 4ac))/2a

So so solve your problem x(x+4) = 21, first expand it into the form above:

x(x + 4) - 21 = 0 Subtract 21 from both sides

x² + 4x - 21 = 0 Now the equation is in the form ax² + bx + c = 0

So using the quadratic formula,

x = (-4² - 4*1*(-21)))/2*1

x = ( -4 ± sqrt(16 + 4*21))/2

x = ( -4 ± sqrt(16 + 84))/2

x = ( -4 ± sqrt(100))/2

x = ( -4 ± 10)/2 = -2 ± 5

So x = -2 + 5 = 3 and x = -2 - 5 = -7

x ( x + 4 ) = 21

To solve this equation , we should first distribute the " x "

By distributing the " x " , you should get

x^2 + 4x = 21 now we can subtract 21 on both sides

By subtracting 21 on both sides , you would get

x^2 + 4x - 21 = 0 Now we can factor ( such as using the x factor which means having two numbers that would have a product of -21 and a sum of 4 )

By factoring the equation , you would get

( x + 7 ) ( x - 3 ) This is just basically x + 7 = 0 and x - 3 = 0

So your answer is x = -7 or 3

x = 3

I noticed when looking at this equation that it was easier to solve than others were making it. I looked at the factors of 21 (3 and 7) and paired them each with the other side of the equation (x=3 and (x+4)=7). To me it was as simple as that.

x(x+4)=21.

To solve for x, we expand left side.

x^2+4x=21.

The left side is made a perfect square by adding 4. So right side also is added 4, to maintain the equality as below:

x^2+4x**+4**=21**+4**

(x+2)^2=25.

We take square root:

x+2=+5 or x+2 =-5

x=5-2=** 3 ** or x= -5-2=**-7.**

This can also be done by factorisation as below:

x(x+4)=21

Expand the left and shift the 21 to left by simple operation of subtraction. Then we are with aquadratic equation in x.

x^2+4x=21.

x^2+**4x**-21=0.

x^2+**7x-3x**-21=0, as the middle term 4x=7x-3x and (7x)(-3x)= -21x^2 , the product of first and last terms:x^2*(-21)

x(x+7)-3(x+7)=0

(x+7)(x-3)=0---->x+7=0 or x-3=0

x+7=0------> x = -7

x-3=0------> x = 3