Solve x^2-8>7 - ScanMath

Evaluate

x^{2} - 8 > 7

Move the expression to the left side

x^{2} - 8 - 7 > 0

Subtract the numbers

x^{2} - 15 > 0

Rewrite the expression

x^{2} - 15 = 0

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

x^{2} = 0 + 15

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

x^{2} = 15

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

x = \pm 15

Separate the equation into 2 possible cases

x = 15 x = - 15

Determine the test intervals using the critical values

x < - 15 - 15 < x < 15 x > 15

Choose a value form each interval

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

To determine if x < - 15 is the solution to the inequality,test if the chosen value x = - 5 satisfies the initial inequality

More Steps

x < - 15 is the solution x_{2} = 0 x_{3} = 5

To determine if - 15 < x < 15 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 15 is the solution - 15 < x < 15 is not a solution x_{3} = 5

To determine if x > 15 is the solution to the inequality,test if the chosen value x = 5 satisfies the initial inequality

More Steps

x < - 15 is the solution - 15 < x < 15 is not a solution x > 15 is the solution

Solution

x \in (- \infty, - 15) \cup (15, + \infty)

Solve the inequality