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What number must be added to the expression below to complete the square x^2+16x=3

User Suchita
by
4.6k points

2 Answers

2 votes

Step-by-step explanation:x

2 + 16 x = 3

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b .

( b 2 ) 2 = ( 8 ) 2

Add the term to each side of the equation.

x 2 + 16 x + ( 8 ) 2 = 3 + ( 8 ) 2

Simplify the equation.

Raise

8

to the power of 2 .

x 2 + 16 x + 64 = 3 + ( 8 ) 2

Simplify 3 + ( 8 ) 2 .

Tap for more steps...

x 2 + 16 x + 64 = 67

Factor the perfect trinomial square into ( x + 8 ) 2 .

( x+ 8 ) 2 = 67

Solve the equation for x .

Tap for fewer steps...

Take the square root of each side of the equation to set up the solution for x .

( x + 8 ) 2 ⋅ 1 2 = ± √ 67

Remove the perfect root factor

x + 8

under the radical to solve for x .

x + 8 = ± √ 67

Remove parentheses.

x + 8 = ± √ 67

Subtract

8

from both sides of the equation.

x = ± √ 67 − 8

The result can be shown in multiple forms.

Exact Form:

x = ± √67 − 8 x 2 + 16 x = 3

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b .

( b 2 ) 2 = ( 8 ) 2

Add the term to each side of the equation.

x 2 + 16 x + ( 8 ) 2 = 3 + ( 8 ) 2

Simplify the equation.

Raise

8

to the power of 2 .

x 2 + 16 x+ 64 = 3 + ( 8 ) 2

Simplify 3 + ( 8 ) 2 .

Tap for more steps...

x 2 + 16 x + 64 = 67

Factor the perfect trinomial square into ( x + 8 ) 2 .

( x + 8 ) 2 = 67

Solve the equation for x .

Take the square root of each side of the equation to set up the solution for x .

( x + 8 ) 2 ⋅ 1 2 = ± √ 67

Remove the perfect root factor

x + 8

under the radical to solve for x .

x + 8 = ± √ 67

Remove parentheses.

x + 8 = ± √ 67

Subtract

8

from both sides of the equation.

x = ± √ 67 − 8

The result can be shown in multiple forms.

Exact Form:

x = ± √ 67 − 8

Decimal Form:

x = 0.18535277 … , − 16.18535277 …

x 2 + 16 x = 3

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b .

( b 2 ) 2 = ( 8 ) 2

Add the term to each side of the equation.

x 2 + 16 x + ( 8 ) 2 = 3 + ( 8 ) 2

Simplify the equation.

Raise

8

to the power of 2 .

x 2 + 16 x + 64 = 3 + ( 8 ) 2

Simplify 3 + ( 8 ) 2 .

Raise

8

to the power of 2 .

x 2 + 16 x + 64 = 3 + 64

Add

3

and 64 .

x 2 + 16 x + 64 = 67

Factor the perfect trinomial square into ( x + 8 ) 2 .

( x + 8 ) 2 = 67

Solve the equation for x .

Take the square root of each side of the equation to set up the solution for x .

( x + 8 ) 2 ⋅ 1 2 = ± √ 67

Remove the perfect root factor

x + 8

under the radical to solve for x .

x + 8 = ± √ 67

Remove parentheses.

x + 8 = ± √ 67

Subtract

8

from both sides of the equation.

x = ± √ 67 − 8

The result can be shown in multiple forms.

Exact Form:

x = ± √ 67 − 8

Decimal Form:

x = 0.18535277 … , − 16.18535277 …

Decimal Form:

x = 0.18535277 … , − 16.18535277 …

User Lajuette
by
4.4k points
2 votes

Answer:

Explanation:

You need to move the 3 over to the left to make standard form.

x^2+16x-3=0 answer by completing the square

x= ± √67 -8

User Crates
by
4.7k points