Solve 5x^(2)-7x=34

Question

Solve the quadratic equation

x_{1} = - 2, x_{2} = \frac{17}{5}

Alternative Form

x_{1} = - 2, x_{2} = 3.4

Evaluate

5 x^{2} - 7 x = 34

Move the expression to the left side

5 x^{2} - 7 x - 34 = 0

Factor the expression

More Steps

Evaluate

5 x^{2} - 7 x - 34

Rewrite the expression

5 x^{2} + (- 17 + 10) x - 34

Calculate

5 x^{2} - 17 x + 10 x - 34

Rewrite the expression

x \times 5 x - x \times 17 + 2 \times 5 x - 2 \times 17

Factor out x from the expression

x (5 x - 17) + 2 \times 5 x - 2 \times 17

Factor out 2 from the expression

x (5 x - 17) + 2 (5 x - 17)

Factor out 5 x - 17 from the expression

(x + 2) (5 x - 17)

(x + 2) (5 x - 17) = 0

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

5 x - 17 = 0 x + 2 = 0

Solve the equation for x

More Steps

Evaluate

5 x - 17 = 0

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

5 x = 0 + 17

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

5 x = 17

Divide both sides

\frac{5 x}{5} = \frac{17}{5}

Divide the numbers

x = \frac{17}{5}

x = \frac{17}{5} x + 2 = 0

Solve the equation for x

More Steps

Evaluate

x + 2 = 0

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

x = 0 - 2

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

x = - 2

x = \frac{17}{5} x = - 2

Solution

x_{1} = - 2, x_{2} = \frac{17}{5}

Alternative Form

x_{1} = - 2, x_{2} = 3.4

Show Solution