Question

Solve for x:

8x^2−3=2

Please provide a step-by-step answer.

Answer 1

`x = \boxed{ (√(10))/(4) , - (√(10))/(4) }`

Explanation:

We can solve this question by using the method of finding the square root.

The given equation is:

`8x ^ { 2 } -3=2`

Add 3 to both the sides of the equation.

`8x^(2)=2+3`

Now, add 2 & 3 to get 5.

`8x^(2)=5`

Dividing both the sides of the equation by 8, we get...

`x^(2)=(5)/(8)`

Now, take the square root of both the sides of the equation...

`x =\sqrt{ ( 5 )/( 8 ) } \\x = (√(5))/(√(8)) \\`

Rationalize the denominator.

`x = (√(5))/(2√(2)) \\x = (√(5)√(2))/(2\left(√(2)\right)^(2)) \\x = (√(5)√(2))/(2* 2) \\x = (√(10))/(2* 2) \\x = \boxed{ (√(10))/(4) , - (√(10))/(4) }`

`\rule{200}{3}`

• The value of x =
  `\boxed{ (√(10))/(4) , - (√(10))/(4) }`

`\rule{200}{3}`

Hope this helps!

Answer 2

`\rf x=(√(10))/(4),\:x=-(√(10))/(4)`

step wise explanation:

• 
  `\rf 8x^2 - 3=2`

change sides:

• 
  `\rf 8x^2 =2+3`

simplify

• 
  `\sf 8x^2 = 5`

change sides:

• 
  `\sf x^2 = (5)/(8)`

changing square to square root:

• 
  `x = \pm \sqrt{(5)/(8) }`

normal answer:

• 
  `\rf \sqrt{(5)/(8) } \ \ or -\sqrt{(5)/(8) }`

apply radical rule of

• 
  `\rf (√(5) )/(√(8) ) } \ \ or \rf -(√(5) )/(√(8) ) }`

• 
  `\sf (√(5))/(2√(2)) \ \ or \ \ \sf -(√(5))/(2√(2))`

rationalise:

• 
  `(√(5)√(2))/(2√(2)√(2)) \ \ or \ - (√(5)√(2))/(2√(2)√(2))`

final answer, simplified:

• 
  `\rf x=(√(10))/(4),\:x=-(√(10))/(4)`