Solve 212-19b^2 - ScanMath

Question

Find the roots

b_{1} = - \frac{2 1007}{19}, b_{2} = \frac{2 1007}{19}

Alternative Form

b_{1} \approx - 3.340344, b_{2} \approx 3.340344

Evaluate

212 - 19 b^{2}

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

212 - 19 b^{2} = 0

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

- 19 b^{2} = 0 - 212

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

- 19 b^{2} = - 212

Change the signs on both sides of the equation

19 b^{2} = 212

Divide both sides

\frac{19 b ^{2}}{19} = \frac{212}{19}

Divide the numbers

b^{2} = \frac{212}{19}

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

b = \pm \frac{212}{19}

Simplify the expression

More Steps

Evaluate

\frac{212}{19}

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

\frac{212}{19}

Simplify the radical expression

More Steps

Evaluate

212

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

4 \times 53

Write the number in exponential form with the base of 2

2^{2} \times 53

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

2^{2} \times 53

Reduce the index of the radical and exponent with 2

253

\frac{2 53}{19}

Multiply by the Conjugate

\frac{2 53 \times 19}{19 \times 19}

Multiply the numbers

More Steps

Evaluate

53 \times 19

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

53 \times 19

Calculate the product

1007

\frac{2 1007}{19 \times 19}

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

\frac{2 1007}{19}

b = \pm \frac{2 1007}{19}

Separate the equation into 2 possible cases

b = \frac{2 1007}{19} b = - \frac{2 1007}{19}

Solution

b_{1} = - \frac{2 1007}{19}, b_{2} = \frac{2 1007}{19}

Alternative Form

b_{1} \approx - 3.340344, b_{2} \approx 3.340344

Show Solution