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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 x1 = 13/15 and x2 = 1/3

Substitute x1 = 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 x1 = 13/15 is the solution of the original equation. Substitute x2 = 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 x2 = 1/3 is the solution of the original equation. After testing we find that the value of x1 and x2 are the solutions of the original equation.