Solve 3100-15q^242

Question

Simplify the expression

3100 - 630 q^{2}

Evaluate

3100 - 15 q^{2} \times 42

Solution

3100 - 630 q^{2}

Show Solution

10 (310 - 63 q^{2})

Evaluate

3100 - 15 q^{2} \times 42

Multiply the terms

3100 - 630 q^{2}

Solution

10 (310 - 63 q^{2})

Show Solution

q_{1} = - \frac{2170}{21}, q_{2} = \frac{2170}{21}

Alternative Form

q_{1} \approx - 2.21825, q_{2} \approx 2.21825

Evaluate

3100 - 15 q^{2} \times 42

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

3100 - 15 q^{2} \times 42 = 0

Multiply the terms

3100 - 630 q^{2} = 0

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

- 630 q^{2} = 0 - 3100

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

- 630 q^{2} = - 3100

Change the signs on both sides of the equation

630 q^{2} = 3100

Divide both sides

\frac{630 q ^{2}}{630} = \frac{3100}{630}

Divide the numbers

q^{2} = \frac{3100}{630}

Cancel out the common factor 10

q^{2} = \frac{310}{63}

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

q = \pm \frac{310}{63}

Simplify the expression

More Steps

Evaluate

\frac{310}{63}

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

\frac{310}{63}

Simplify the radical expression

More Steps

Evaluate

63

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

9 \times 7

Write the number in exponential form with the base of 3

3^{2} \times 7

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

3^{2} \times 7

Reduce the index of the radical and exponent with 2

37

\frac{310}{3 7}

Multiply by the Conjugate

\frac{310 \times 7}{3 7 \times 7}

Multiply the numbers

More Steps

Evaluate

310 \times 7

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

310 \times 7

Calculate the product

2170

\frac{2170}{3 7 \times 7}

Multiply the numbers

More Steps

Evaluate

37 \times 7

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

3 \times 7

Multiply the terms

21

\frac{2170}{21}

q = \pm \frac{2170}{21}

Separate the equation into 2 possible cases

q = \frac{2170}{21} q = - \frac{2170}{21}

Solution

q_{1} = - \frac{2170}{21}, q_{2} = \frac{2170}{21}

Alternative Form

q_{1} \approx - 2.21825, q_{2} \approx 2.21825

Show Solution