Solve b^2-4(1)(5)>0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for b

b \in (- \infty, - 25) \cup (25, + \infty)

Evaluate

b^{2} - 4 \times 1 \times 5 > 0

Multiply the terms

More Steps

b^{2} - 20 > 0

Rewrite the expression

b^{2} - 20 = 0

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

b^{2} = 0 + 20

Removing 0 doesn't change the value,so remove it from the expression

b^{2} = 20

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

b = \pm 20

Simplify the expression

More Steps

b = \pm 25

Separate the equation into 2 possible cases

b = 25 b = - 25

Determine the test intervals using the critical values

b < - 25 - 25 < b < 25 b > 25

Choose a value form each interval

b_{1} = - 5 b_{2} = 0 b_{3} = 5

To determine if b < - 25 is the solution to the inequality,test if the chosen value b = - 5 satisfies the initial inequality

More Steps

b < - 25 is the solution b_{2} = 0 b_{3} = 5

To determine if - 25 < b < 25 is the solution to the inequality,test if the chosen value b = 0 satisfies the initial inequality

More Steps

b < - 25 is the solution - 25 < b < 25 is not a solution b_{3} = 5

To determine if b > 25 is the solution to the inequality,test if the chosen value b = 5 satisfies the initial inequality

More Steps

b < - 25 is the solution - 25 < b < 25 is not a solution b > 25 is the solution

Solution

b \in (- \infty, - 25) \cup (25, + \infty)

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