Solve 3^2 x- 5 =4x^2 - Socratic AI (ScanMath)

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = 1, x_{2} = \frac{5}{4}

Alternative Form

x_{1} = 1, x_{2} = 1.25

Evaluate

3^{2} x - 5 = 4 x^{2}

Evaluate the power

9 x - 5 = 4 x^{2}

Swap the sides

4 x^{2} = 9 x - 5

Move the expression to the left side

4 x^{2} - 9 x + 5 = 0

Factor the expression

More Steps

Evaluate

4 x^{2} - 9 x + 5

Rewrite the expression

4 x^{2} + (- 5 - 4) x + 5

Calculate

4 x^{2} - 5 x - 4 x + 5

Rewrite the expression

x \times 4 x - x \times 5 - 4 x + 5

Factor out x from the expression

x (4 x - 5) - 4 x + 5

Factor out - 1 from the expression

x (4 x - 5) - (4 x - 5)

Factor out 4 x - 5 from the expression

(x - 1) (4 x - 5)

(x - 1) (4 x - 5) = 0

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

4 x - 5 = 0 x - 1 = 0

Solve the equation for x

More Steps

Evaluate

4 x - 5 = 0

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

4 x = 0 + 5

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

4 x = 5

Divide both sides

\frac{4 x}{4} = \frac{5}{4}

Divide the numbers

x = \frac{5}{4}

x = \frac{5}{4} x - 1 = 0

Solve the equation for x

More Steps

Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = \frac{5}{4} x = 1

Solution

x_{1} = 1, x_{2} = \frac{5}{4}

Alternative Form

x_{1} = 1, x_{2} = 1.25

Show Solution