Solve 15x^2-4x^4 - Socratic AI (ScanMath)

Question

Factor the expression

x^{2} (15 - 4 x^{2})

Evaluate

15 x^{2} - 4 x^{4}

Rewrite the expression

x^{2} \times 15 - x^{2} \times 4 x^{2}

Solution

x^{2} (15 - 4 x^{2})

Show Solution

x_{1} = - \frac{15}{2}, x_{2} = 0, x_{3} = \frac{15}{2}

Alternative Form

x_{1} \approx - 1.936492, x_{2} = 0, x_{3} \approx 1.936492

Evaluate

15 x^{2} - 4 x^{4}

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

15 x^{2} - 4 x^{4} = 0

Factor the expression

x^{2} (15 - 4 x^{2}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 15 - 4 x^{2} = 0

The only way a power can be 0 is when the base equals 0

x = 0 15 - 4 x^{2} = 0

Solve the equation

More Steps

Evaluate

15 - 4 x^{2} = 0

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

- 4 x^{2} = 0 - 15

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

- 4 x^{2} = - 15

Change the signs on both sides of the equation

4 x^{2} = 15

Divide both sides

\frac{4 x ^{2}}{4} = \frac{15}{4}

Divide the numbers

x^{2} = \frac{15}{4}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{15}{4}

Simplify the expression

More Steps

Evaluate

\frac{15}{4}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{15}{4}

Simplify the radical expression

\frac{15}{2}

x = \pm \frac{15}{2}

Separate the equation into 2 possible cases

x = \frac{15}{2} x = - \frac{15}{2}

x = 0 x = \frac{15}{2} x = - \frac{15}{2}

Solution

x_{1} = - \frac{15}{2}, x_{2} = 0, x_{3} = \frac{15}{2}

Alternative Form

x_{1} \approx - 1.936492, x_{2} = 0, x_{3} \approx 1.936492

Show Solution