Solve 49-4a^2 - ScanMath

Question

Factor the expression

(7 - 2 a) (7 + 2 a)

Evaluate

49 - 4 a^{2}

Rewrite the expression in exponential form

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

Solution

(7 - 2 a) (7 + 2 a)

Show Solution

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

Alternative Form

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

Evaluate

49 - 4 a^{2}

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

49 - 4 a^{2} = 0

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

- 4 a^{2} = 0 - 49

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

- 4 a^{2} = - 49

Change the signs on both sides of the equation

4 a^{2} = 49

Divide both sides

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

Divide the numbers

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

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

a = \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}

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

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

Show Solution