Solve 36q^6q-5q - Socratic AI (ScanMath)

Question

Simplify the expression

36 q^{7} - 5 q

Evaluate

36 q^{6} \times q - 5 q

Solution

More Steps

Evaluate

36 q^{6} \times q

Multiply the terms with the same base by adding their exponents

36 q^{6 + 1}

Add the numbers

36 q^{7}

36 q^{7} - 5 q

Show Solution

Factor the expression

q (36 q^{6} - 5)

Evaluate

36 q^{6} \times q - 5 q

Multiply

More Steps

Evaluate

36 q^{6} \times q

Multiply the terms with the same base by adding their exponents

36 q^{6 + 1}

Add the numbers

36 q^{7}

36 q^{7} - 5 q

Rewrite the expression

q \times 36 q^{6} - q \times 5

Solution

q (36 q^{6} - 5)

Show Solution

Find the roots

q_{1} = - \frac{6 6480}{6}, q_{2} = 0, q_{3} = \frac{6 6480}{6}

Alternative Form

q_{1} \approx - 0.719633, q_{2} = 0, q_{3} \approx 0.719633

Evaluate

36 q^{6} \times q - 5 q

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

36 q^{6} \times q - 5 q = 0

Multiply

More Steps

Multiply the terms

36 q^{6} \times q

Multiply the terms with the same base by adding their exponents

36 q^{6 + 1}

Add the numbers

36 q^{7}

36 q^{7} - 5 q = 0

Factor the expression

q (36 q^{6} - 5) = 0

Separate the equation into 2 possible cases

q = 0 36 q^{6} - 5 = 0

Solve the equation

More Steps

Evaluate

36 q^{6} - 5 = 0

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

36 q^{6} = 0 + 5

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

36 q^{6} = 5

Divide both sides

\frac{36 q ^{6}}{36} = \frac{5}{36}

Divide the numbers

q^{6} = \frac{5}{36}

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

q = \pm 6 \frac{5}{36}

Simplify the expression

More Steps

Evaluate

6 \frac{5}{36}

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

\frac{6 5}{6 36}

Simplify the radical expression

\frac{6 5}{3 6}

Multiply by the Conjugate

\frac{6 5 \times 3 6 ^{2}}{3 6 \times 3 6 ^{2}}

Simplify

\frac{6 5 \times 3 36}{3 6 \times 3 6 ^{2}}

Multiply the numbers

\frac{6 6480}{3 6 \times 3 6 ^{2}}

Multiply the numbers

\frac{6 6480}{6}

q = \pm \frac{6 6480}{6}

Separate the equation into 2 possible cases

q = \frac{6 6480}{6} q = - \frac{6 6480}{6}

q = 0 q = \frac{6 6480}{6} q = - \frac{6 6480}{6}

Solution

q_{1} = - \frac{6 6480}{6}, q_{2} = 0, q_{3} = \frac{6 6480}{6}

Alternative Form

q_{1} \approx - 0.719633, q_{2} = 0, q_{3} \approx 0.719633

Show Solution

36q^6q 5q

Simplify the expression

Factor the expression

Find the roots