Solve 4x^2=13x-3 - ScanMath

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

x_{1} = 0.25, x_{2} = 3

Evaluate

4 x^{2} = 13 x - 3

Move the expression to the left side

4 x^{2} - 13 x + 3 = 0

Factor the expression

More Steps

Evaluate

4 x^{2} - 13 x + 3

Rewrite the expression

4 x^{2} + (- 1 - 12) x + 3

Calculate

4 x^{2} - x - 12 x + 3

Rewrite the expression

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

Factor out x from the expression

x (4 x - 1) - 3 \times 4 x + 3

Factor out - 3 from the expression

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

Factor out 4 x - 1 from the expression

(x - 3) (4 x - 1)

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

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

x - 3 = 0 4 x - 1 = 0

Solve the equation for x

More Steps

Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 3 4 x - 1 = 0

Solve the equation for x

More Steps

Evaluate

4 x - 1 = 0

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

4 x = 0 + 1

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

4 x = 1

Divide both sides

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

Divide the numbers

x = \frac{1}{4}

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

Solution

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

Alternative Form

x_{1} = 0.25, x_{2} = 3

Show Solution