Solve 3x 12x -10 - ScanMath

Question

Simplify the expression

36 x^{2} - 10

Evaluate

3 x \times 12 x - 10

Solution

More Steps

Evaluate

3 x \times 12 x

Multiply the terms

36 x \times x

Multiply the terms

36 x^{2}

36 x^{2} - 10

Show Solution

Factor the expression

2 (18 x^{2} - 5)

Evaluate

3 x \times 12 x - 10

Multiply

More Steps

Evaluate

3 x \times 12 x

Multiply the terms

36 x \times x

Multiply the terms

36 x^{2}

36 x^{2} - 10

Solution

2 (18 x^{2} - 5)

Show Solution

Find the roots

x_{1} = - \frac{10}{6}, x_{2} = \frac{10}{6}

Alternative Form

x_{1} \approx - 0.527046, x_{2} \approx 0.527046

Evaluate

3 x \times 12 x - 10

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

3 x \times 12 x - 10 = 0

Multiply

More Steps

Multiply the terms

3 x \times 12 x

Multiply the terms

36 x \times x

Multiply the terms

36 x^{2}

36 x^{2} - 10 = 0

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

36 x^{2} = 0 + 10

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

36 x^{2} = 10

Divide both sides

\frac{36 x ^{2}}{36} = \frac{10}{36}

Divide the numbers

x^{2} = \frac{10}{36}

Cancel out the common factor 2

x^{2} = \frac{5}{18}

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

x = \pm \frac{5}{18}

Simplify the expression

More Steps

Evaluate

\frac{5}{18}

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

\frac{5}{18}

Simplify the radical expression

More Steps

Evaluate

18

Write the expression as a product where the root of one of the factors can be evaluated

9 \times 2

Write the number in exponential form with the base of 3

3^{2} \times 2

The root of a product is equal to the product of the roots of each factor

3^{2} \times 2

Reduce the index of the radical and exponent with 2

32

\frac{5}{3 2}

Multiply by the Conjugate

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

Multiply the numbers

More Steps

Evaluate

5 \times 2

The product of roots with the same index is equal to the root of the product

5 \times 2

Calculate the product

10

\frac{10}{3 2 \times 2}

Multiply the numbers

More Steps

Evaluate

32 \times 2

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

3 \times 2

Multiply the terms

6

\frac{10}{6}

x = \pm \frac{10}{6}

Separate the equation into 2 possible cases

x = \frac{10}{6} x = - \frac{10}{6}

Solution

x_{1} = - \frac{10}{6}, x_{2} = \frac{10}{6}

Alternative Form

x_{1} \approx - 0.527046, x_{2} \approx 0.527046

Show Solution