Solve 8a^2-4(2a-4)^2>0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for a

- 22 + 4 < a < 22 + 4

Alternative Form

a \in (- 22 + 4, 22 + 4)

Evaluate

8 a^{2} - 4 (2 a - 4)^{2} > 0

Rearrange the terms

- 8 a^{2} + 64 a - 64 > 0

Rewrite the expression

- 8 a^{2} + 64 a - 64 = 0

Add or subtract both sides

- 8 a^{2} + 64 a = 64

Divide both sides

\frac{- 8 a ^{2} + 64 a}{- 8} = \frac{64}{- 8}

Evaluate

a^{2} - 8 a = - 8

Add the same value to both sides

a^{2} - 8 a + 16 = - 8 + 16

Simplify the expression

(a - 4)^{2} = 8

Take the root of both sides of the equation and remember to use both positive and negative roots

a - 4 = \pm 8

Simplify the expression

a - 4 = \pm 22

Separate the equation into 2 possible cases

a - 4 = 22 a - 4 = - 22

Move the constant to the right-hand side and change its sign

a = 22 + 4 a - 4 = - 22

Move the constant to the right-hand side and change its sign

a = 22 + 4 a = - 22 + 4

Determine the test intervals using the critical values

a < - 22 + 4 - 22 + 4 < a < 22 + 4 a > 22 + 4

Choose a value form each interval

a_{1} = 0 a_{2} = 4 a_{3} = 8

To determine if a < - 22 + 4 is the solution to the inequality,test if the chosen value a = 0 satisfies the initial inequality

More Steps

a < - 22 + 4 is not a solution a_{2} = 4 a_{3} = 8

To determine if - 22 + 4 < a < 22 + 4 is the solution to the inequality,test if the chosen value a = 4 satisfies the initial inequality

More Steps

a < - 22 + 4 is not a solution - 22 + 4 < a < 22 + 4 is the solution a_{3} = 8

To determine if a > 22 + 4 is the solution to the inequality,test if the chosen value a = 8 satisfies the initial inequality

More Steps

a < - 22 + 4 is not a solution - 22 + 4 < a < 22 + 4 is the solution a > 22 + 4 is not a solution

Solution

- 22 + 4 < a < 22 + 4

Alternative Form

a \in (- 22 + 4, 22 + 4)

Show Solution