Solve p* p-687≤84

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for p

- 771 \leq p \leq 771

Alternative Form

p \in [- 771, 771]

Evaluate

p \times p - 687 \leq 84

Multiply the terms

p^{2} - 687 \leq 84

Move the expression to the left side

p^{2} - 687 - 84 \leq 0

Subtract the numbers

p^{2} - 771 \leq 0

Rewrite the expression

p^{2} - 771 = 0

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

p^{2} = 0 + 771

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

p^{2} = 771

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

p = \pm 771

Separate the equation into 2 possible cases

p = 771 p = - 771

Determine the test intervals using the critical values

p < - 771 - 771 < p < 771 p > 771

Choose a value form each interval

p_{1} = - 29 p_{2} = 0 p_{3} = 29

To determine if p < - 771 is the solution to the inequality,test if the chosen value p = - 29 satisfies the initial inequality

More Steps

p < - 771 is not a solution p_{2} = 0 p_{3} = 29

To determine if - 771 < p < 771 is the solution to the inequality,test if the chosen value p = 0 satisfies the initial inequality

More Steps

p < - 771 is not a solution - 771 < p < 771 is the solution p_{3} = 29

To determine if p > 771 is the solution to the inequality,test if the chosen value p = 29 satisfies the initial inequality

More Steps

p < - 771 is not a solution - 771 < p < 771 is the solution p > 771 is not a solution

The original inequality is a nonstrict inequality,so include the critical value in the solution

- 771 \leq p \leq 771 is the solution

Solution

- 771 \leq p \leq 771

Alternative Form

p \in [- 771, 771]

Show Solution