Solve 2x^(2)-10x 10<0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

0 < x < 50

Alternative Form

x \in (0, 50)

Evaluate

2 x^{2} - 10 x \times 10 < 0

Multiply the terms

2 x^{2} - 100 x < 0

Rewrite the expression

2 x^{2} - 100 x = 0

Factor the expression

More Steps

2 x (x - 50) = 0

When the product of factors equals 0,at least one factor is 0

2 x = 0 x - 50 = 0

Solve the equation for x

x = 0 x - 50 = 0

Solve the equation for x

More Steps

x = 0 x = 50

Determine the test intervals using the critical values

x < 0 0 < x < 50 x > 50

Choose a value form each interval

x_{1} = - 1 x_{2} = 25 x_{3} = 51

To determine if x < 0 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < 0 is not a solution x_{2} = 25 x_{3} = 51

To determine if 0 < x < 50 is the solution to the inequality,test if the chosen value x = 25 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < 50 is the solution x_{3} = 51

To determine if x > 50 is the solution to the inequality,test if the chosen value x = 51 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < 50 is the solution x > 50 is not a solution

Solution

0 < x < 50

Alternative Form

x \in (0, 50)

Show Solution