Solve r^210-9 - Socratic AI (ScanMath)

Question

Simplify the expression

10 r^{2} - 9

Evaluate

r^{2} \times 10 - 9

Solution

10 r^{2} - 9

Show Solution

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

Alternative Form

r_{1} \approx - 0.948683, r_{2} \approx 0.948683

Evaluate

r^{2} \times 10 - 9

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

r^{2} \times 10 - 9 = 0

Use the commutative property to reorder the terms

10 r^{2} - 9 = 0

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

10 r^{2} = 0 + 9

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

10 r^{2} = 9

Divide both sides

\frac{10 r ^{2}}{10} = \frac{9}{10}

Divide the numbers

r^{2} = \frac{9}{10}

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

r = \pm \frac{9}{10}

Simplify the expression

More Steps

Evaluate

\frac{9}{10}

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

\frac{9}{10}

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{3}{10}

Multiply by the Conjugate

\frac{3 10}{10 \times 10}

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

\frac{3 10}{10}

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

r_{1} \approx - 0.948683, r_{2} \approx 0.948683

Show Solution