Solve k*k-314<1 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for k

- 335 < k < 335

Alternative Form

k \in (- 335, 335)

Evaluate

k \times k - 314 < 1

Multiply the terms

k^{2} - 314 < 1

Move the expression to the left side

k^{2} - 314 - 1 < 0

Subtract the numbers

k^{2} - 315 < 0

Rewrite the expression

k^{2} - 315 = 0

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

k^{2} = 0 + 315

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

k^{2} = 315

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

k = \pm 315

Simplify the expression

More Steps

k = \pm 335

Separate the equation into 2 possible cases

k = 335 k = - 335

Determine the test intervals using the critical values

k < - 335 - 335 < k < 335 k > 335

Choose a value form each interval

k_{1} = - 19 k_{2} = 0 k_{3} = 19

To determine if k < - 335 is the solution to the inequality,test if the chosen value k = - 19 satisfies the initial inequality

More Steps

k < - 335 is not a solution k_{2} = 0 k_{3} = 19

To determine if - 335 < k < 335 is the solution to the inequality,test if the chosen value k = 0 satisfies the initial inequality

More Steps

k < - 335 is not a solution - 335 < k < 335 is the solution k_{3} = 19

To determine if k > 335 is the solution to the inequality,test if the chosen value k = 19 satisfies the initial inequality

More Steps

k < - 335 is not a solution - 335 < k < 335 is the solution k > 335 is not a solution

Solution

- 335 < k < 335

Alternative Form

k \in (- 335, 335)

Show Solution