Solve 2 (4x^2) - 8 < -5x - 30

Evaluate

2 \times 4 x^{2} - 8 < - 5 x - 30

Multiply the numbers

8 x^{2} - 8 < - 5 x - 30

Move the expression to the left side

8 x^{2} - 8 - (- 5 x - 30) < 0

Subtract the terms

More Steps

8 x^{2} + 22 + 5 x < 0

Rewrite the expression

8 x^{2} + 22 + 5 x = 0

Add or subtract both sides

8 x^{2} + 5 x = - 22

Divide both sides

\frac{8 x ^{2} + 5 x}{8} = \frac{- 22}{8}

Evaluate

x^{2} + \frac{5}{8} x = - \frac{11}{4}

Add the same value to both sides

x^{2} + \frac{5}{8} x + \frac{25}{256} = - \frac{11}{4} + \frac{25}{256}

Simplify the expression

(x + \frac{5}{16})^{2} = - \frac{679}{256}

Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is false for any value of x

x \in / R

There are no key numbers,so choose any value to test,for example x = 0

x = 0

Solution

More Steps

x \in \emptyset

Alternative Form

No solution

Solve the inequality