4x {}^(2) = x {}^(2) + 4 ​

Question

`4x {}^(2) = x {}^(2) + 4`
​

Answer 1

x = 1.155

x = -1.155

Explanation:

4x² = x² + 4

i) move variable to the left-hand side and change its sign

4x² - x² = 4

ii) collect like terms

3x² = 4

iii) divide both sides of the equation by 3

`\frac{ {3x}^(2) }{3} = (4)/(3)`

`{x}^(2) = (4)/(3)`

iv) take the square root to the opposite side of the equation and remember to use

positive and negative roots

`x = + - \sqrt{ (4)/( 3) }`

v) the equation has two solutions. write the solutions, one with a '+' sign and another with a '-' sign

`x = \sqrt{ (4)/(3) } \: or \: 1.155`

`x = - \sqrt{ (4)/(3) } \: or - 1.155`