Solve 4x^2 -49 - ScanMath

Question

Factor the expression

(2 x - 7) (2 x + 7)

Evaluate

4 x^{2} - 49

Rewrite the expression in exponential form

(2 x)^{2} - 7^{2}

Solution

(2 x - 7) (2 x + 7)

Show Solution

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

Alternative Form

x_{1} = - 3.5, x_{2} = 3.5

Evaluate

4 x^{2} - 49

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

4 x^{2} - 49 = 0

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

4 x^{2} = 0 + 49

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

4 x^{2} = 49

Divide both sides

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

Divide the numbers

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

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

x = \pm \frac{49}{4}

Simplify the expression

More Steps

Evaluate

\frac{49}{4}

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

\frac{49}{4}

Simplify the radical expression

More Steps

Evaluate

49

Write the number in exponential form with the base of 7

7^{2}

Reduce the index of the radical and exponent with 2

7

\frac{7}{4}

Simplify the radical expression

More Steps

Evaluate

4

Write the number in exponential form with the base of 2

2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{7}{2}

x = \pm \frac{7}{2}

Separate the equation into 2 possible cases

x = \frac{7}{2} x = - \frac{7}{2}

Solution

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

Alternative Form

x_{1} = - 3.5, x_{2} = 3.5

Show Solution