Solve 1/2(-6x^6) 10=-9x^6(x^2) - Socratic AI (ScanMath)

Question

Solve the equation

x_{1} = - \frac{30}{3}, x_{2} = 0, x_{3} = \frac{30}{3}

Alternative Form

x_{1} \approx - 1.825742, x_{2} = 0, x_{3} \approx 1.825742

Evaluate

\frac{1}{2} (- 6 x^{6}) \times 10 = - 9 x^{6} \times x^{2}

Multiply

More Steps

Evaluate

\frac{1}{2} (- 6 x^{6}) \times 10

Rewrite the expression

- \frac{1}{2} \times 6 x^{6} \times 10

Multiply the terms

More Steps

Evaluate

\frac{1}{2} \times 6 \times 10

Multiply the terms

3 \times 10

Multiply the numbers

30

- 30 x^{6}

- 30 x^{6} = - 9 x^{6} \times x^{2}

Multiply

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Evaluate

- 9 x^{6} \times x^{2}

Multiply the terms with the same base by adding their exponents

- 9 x^{6 + 2}

Add the numbers

- 9 x^{8}

- 30 x^{6} = - 9 x^{8}

Add or subtract both sides

- 30 x^{6} - (- 9 x^{8}) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 30 x^{6} + 9 x^{8} = 0

Factor the expression

3 x^{6} (- 10 + 3 x^{2}) = 0

Divide both sides

x^{6} (- 10 + 3 x^{2}) = 0

Separate the equation into 2 possible cases

x^{6} = 0 - 10 + 3 x^{2} = 0

The only way a power can be 0 is when the base equals 0

x = 0 - 10 + 3 x^{2} = 0

Solve the equation

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Evaluate

- 10 + 3 x^{2} = 0

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

3 x^{2} = 0 + 10

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

3 x^{2} = 10

Divide both sides

\frac{3 x ^{2}}{3} = \frac{10}{3}

Divide the numbers

x^{2} = \frac{10}{3}

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

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

Simplify the expression

More Steps

Evaluate

\frac{10}{3}

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

\frac{10}{3}

Multiply by the Conjugate

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

Multiply the numbers

\frac{30}{3 \times 3}

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

\frac{30}{3}

x = \pm \frac{30}{3}

Separate the equation into 2 possible cases

x = \frac{30}{3} x = - \frac{30}{3}

x = 0 x = \frac{30}{3} x = - \frac{30}{3}

Solution

x_{1} = - \frac{30}{3}, x_{2} = 0, x_{3} = \frac{30}{3}

Alternative Form

x_{1} \approx - 1.825742, x_{2} = 0, x_{3} \approx 1.825742

Show Solution

1/2( 6x^6) 10= 9x^6(x^2)

Solve the equation

Graph