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## Solve quadratic equation by root extracion method

Question

Solve the quadratic equation 9 (5x - 3)^{2} = 16

Solution

- 9 (5x - 3)
^{2}= 16 - both side of the equation divide by 9
- (5x - 3)
^{2}= 16/9 - apply the square root to both side of the equation
- 5x - 3 = + - square root of 16/9
- 5x - 3 = + - 4/3 [note: square root of 16/9 = + - 4/3]
- so, we get two equation, one is 5x - 3 = 4/3, the other one is 5x - 3 = -4/3
- solve 5x - 3 = 4/3
- move the number 3 to the right side of the equation, the negative 3 change to positive 3
- 5x = 3 + 4/3
- make the same denominator
- 5x = 9/3 + 4/3
- add two fractions with the same denorminator, keep the denominator and add two numerators
- 5x = 13/3
- both side of the equation divide by 5
- x = 13/15
- Solve 5x - 3 = -4/3
- 5x = 3 - 4/3
- 5x = 9/3 - 4/3
- 5x = 5/3
- both side of the equation divide by 5
- x = 1/3
- so, we get x
_{1}= 13/15 and x_{2}= 1/3

Substitute x_{1} = 13/15 into the original equation to verify if the left side of the equation is equal to the right side of the equation. If yes, then the value of
x_{1} = 13/15 is the solution of the original equation. Substitute x_{2} = 1/3 into the original equation to verify if the left side of the equation is equal to the
right side of the equation. If yes, then the value of x_{2} = 1/3 is the solution of the original equation. After testing we find that the value of x_{1} and
x_{2} are the solutions of the original equation.