Solve x^2 = 7x^4 - ScanMath

Question

Solve the equation

x_{1} = - \frac{7}{7}, x_{2} = 0, x_{3} = \frac{7}{7}

Alternative Form

x_{1} \approx - 0.377964, x_{2} = 0, x_{3} \approx 0.377964

Evaluate

x^{2} = 7 x^{4}

Move the expression to the left side

x^{2} - 7 x^{4} = 0

Factor the expression

x^{2} (1 - 7 x^{2}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 1 - 7 x^{2} = 0

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

x = 0 1 - 7 x^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 7 x^{2} = 0

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

- 7 x^{2} = 0 - 1

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

- 7 x^{2} = - 1

Change the signs on both sides of the equation

7 x^{2} = 1

Divide both sides

\frac{7 x ^{2}}{7} = \frac{1}{7}

Divide the numbers

x^{2} = \frac{1}{7}

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

x = \pm \frac{1}{7}

Simplify the expression

More Steps

Evaluate

\frac{1}{7}

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

\frac{1}{7}

Simplify the radical expression

\frac{1}{7}

Multiply by the Conjugate

\frac{7}{7 \times 7}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{7}{7}

x = \pm \frac{7}{7}

Separate the equation into 2 possible cases

x = \frac{7}{7} x = - \frac{7}{7}

x = 0 x = \frac{7}{7} x = - \frac{7}{7}

Solution

x_{1} = - \frac{7}{7}, x_{2} = 0, x_{3} = \frac{7}{7}

Alternative Form

x_{1} \approx - 0.377964, x_{2} = 0, x_{3} \approx 0.377964

Show Solution