Solve (49 x^2 - 1/4)

Question

Factor the expression

\frac{1}{4} (14 x - 1) (14 x + 1)

Evaluate

49 x^{2} - \frac{1}{4}

Solution

\frac{1}{4} (14 x - 1) (14 x + 1)

Show Solution

x_{1} = - \frac{1}{14}, x_{2} = \frac{1}{14}

Alternative Form

x_{1} = - 0.0 \dot{7} 1428 \dot{5}, x_{2} = 0.0 \dot{7} 1428 \dot{5}

Evaluate

(49 x^{2} - \frac{1}{4})

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

49 x^{2} - \frac{1}{4} = 0

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

49 x^{2} = 0 + \frac{1}{4}

Add the terms

49 x^{2} = \frac{1}{4}

Multiply by the reciprocal

49 x^{2} \times \frac{1}{49} = \frac{1}{4} \times \frac{1}{49}

Multiply

x^{2} = \frac{1}{4} \times \frac{1}{49}

Multiply

More Steps

Evaluate

\frac{1}{4} \times \frac{1}{49}

To multiply the fractions,multiply the numerators and denominators separately

\frac{1}{4 \times 49}

Multiply the numbers

\frac{1}{196}

x^{2} = \frac{1}{196}

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

x = \pm \frac{1}{196}

Simplify the expression

More Steps

Evaluate

\frac{1}{196}

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

\frac{1}{196}

Simplify the radical expression

\frac{1}{196}

Simplify the radical expression

More Steps

Evaluate

196

Write the number in exponential form with the base of 14

1 4^{2}

Reduce the index of the radical and exponent with 2

14

\frac{1}{14}

x = \pm \frac{1}{14}

Separate the equation into 2 possible cases

x = \frac{1}{14} x = - \frac{1}{14}

Solution

x_{1} = - \frac{1}{14}, x_{2} = \frac{1}{14}

Alternative Form

x_{1} = - 0.0 \dot{7} 1428 \dot{5}, x_{2} = 0.0 \dot{7} 1428 \dot{5}

Show Solution