Solve 8x^2 - 10x + 3

Question

Factor the expression

(2 x - 1) (4 x - 3)

Evaluate

8 x^{2} - 10 x + 3

Rewrite the expression

8 x^{2} + (- 6 - 4) x + 3

Calculate

8 x^{2} - 6 x - 4 x + 3

Rewrite the expression

2 x \times 4 x - 2 x \times 3 - 4 x + 3

Factor out 2 x from the expression

2 x (4 x - 3) - 4 x + 3

Factor out - 1 from the expression

2 x (4 x - 3) - (4 x - 3)

Solution

(2 x - 1) (4 x - 3)

Show Solution

x_{1} = \frac{1}{2}, x_{2} = \frac{3}{4}

Alternative Form

x_{1} = 0.5, x_{2} = 0.75

Evaluate

8 x^{2} - 10 x + 3

To find the roots of the expression,set the expression equal to 0

8 x^{2} - 10 x + 3 = 0

Factor the expression

More Steps

Evaluate

8 x^{2} - 10 x + 3

Rewrite the expression

8 x^{2} + (- 6 - 4) x + 3

Calculate

8 x^{2} - 6 x - 4 x + 3

Rewrite the expression

2 x \times 4 x - 2 x \times 3 - 4 x + 3

Factor out 2 x from the expression

2 x (4 x - 3) - 4 x + 3

Factor out - 1 from the expression

2 x (4 x - 3) - (4 x - 3)

Factor out 4 x - 3 from the expression

(2 x - 1) (4 x - 3)

(2 x - 1) (4 x - 3) = 0

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

2 x - 1 = 0 4 x - 3 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 1 = 0

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

2 x = 0 + 1

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

2 x = 1

Divide both sides

\frac{2 x}{2} = \frac{1}{2}

Divide the numbers

x = \frac{1}{2}

x = \frac{1}{2} 4 x - 3 = 0

Solve the equation for x

More Steps

Evaluate

4 x - 3 = 0

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

4 x = 0 + 3

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

4 x = 3

Divide both sides

\frac{4 x}{4} = \frac{3}{4}

Divide the numbers

x = \frac{3}{4}

x = \frac{1}{2} x = \frac{3}{4}

Solution

x_{1} = \frac{1}{2}, x_{2} = \frac{3}{4}

Alternative Form

x_{1} = 0.5, x_{2} = 0.75

Show Solution