Solve 100-9x^2 - ScanMath

Question

Factor the expression

(10 - 3 x) (10 + 3 x)

Evaluate

100 - 9 x^{2}

Rewrite the expression in exponential form

1 0^{2} - (3 x)^{2}

Solution

(10 - 3 x) (10 + 3 x)

Show Solution

x_{1} = - \frac{10}{3}, x_{2} = \frac{10}{3}

Alternative Form

x_{1} = - 3. \dot{3}, x_{2} = 3. \dot{3}

Evaluate

100 - 9 x^{2}

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

100 - 9 x^{2} = 0

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

- 9 x^{2} = 0 - 100

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

- 9 x^{2} = - 100

Change the signs on both sides of the equation

9 x^{2} = 100

Divide both sides

\frac{9 x ^{2}}{9} = \frac{100}{9}

Divide the numbers

x^{2} = \frac{100}{9}

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

x = \pm \frac{100}{9}

Simplify the expression

More Steps

Evaluate

\frac{100}{9}

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

\frac{100}{9}

Simplify the radical expression

More Steps

Evaluate

100

Write the number in exponential form with the base of 10

1 0^{2}

Reduce the index of the radical and exponent with 2

10

\frac{10}{9}

Simplify the radical expression

More Steps

Evaluate

9

Write the number in exponential form with the base of 3

3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{10}{3}

x = \pm \frac{10}{3}

Separate the equation into 2 possible cases

x = \frac{10}{3} x = - \frac{10}{3}

Solution

x_{1} = - \frac{10}{3}, x_{2} = \frac{10}{3}

Alternative Form

x_{1} = - 3. \dot{3}, x_{2} = 3. \dot{3}

Show Solution