Solve b14b-2022 - ScanMath

Question

Simplify the expression

14 b^{2} - 2022

Evaluate

b \times 14 b - 2022

Solution

More Steps

Evaluate

b \times 14 b

Multiply the terms

b^{2} \times 14

Use the commutative property to reorder the terms

14 b^{2}

14 b^{2} - 2022

Show Solution

2 (7 b^{2} - 1011)

Evaluate

b \times 14 b - 2022

Multiply

More Steps

Evaluate

b \times 14 b

Multiply the terms

b^{2} \times 14

Use the commutative property to reorder the terms

14 b^{2}

14 b^{2} - 2022

Solution

2 (7 b^{2} - 1011)

Show Solution

b_{1} = - \frac{7077}{7}, b_{2} = \frac{7077}{7}

Alternative Form

b_{1} \approx - 12.017844, b_{2} \approx 12.017844

Evaluate

b \times 14 b - 2022

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

b \times 14 b - 2022 = 0

Multiply

More Steps

Multiply the terms

b \times 14 b

Multiply the terms

b^{2} \times 14

Use the commutative property to reorder the terms

14 b^{2}

14 b^{2} - 2022 = 0

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

14 b^{2} = 0 + 2022

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

14 b^{2} = 2022

Divide both sides

\frac{14 b ^{2}}{14} = \frac{2022}{14}

Divide the numbers

b^{2} = \frac{2022}{14}

Cancel out the common factor 2

b^{2} = \frac{1011}{7}

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

b = \pm \frac{1011}{7}

Simplify the expression

More Steps

Evaluate

\frac{1011}{7}

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

\frac{1011}{7}

Multiply by the Conjugate

\frac{1011 \times 7}{7 \times 7}

Multiply the numbers

More Steps

Evaluate

1011 \times 7

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

1011 \times 7

Calculate the product

7077

\frac{7077}{7 \times 7}

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

\frac{7077}{7}

b = \pm \frac{7077}{7}

Separate the equation into 2 possible cases

b = \frac{7077}{7} b = - \frac{7077}{7}

Solution

b_{1} = - \frac{7077}{7}, b_{2} = \frac{7077}{7}

Alternative Form

b_{1} \approx - 12.017844, b_{2} \approx 12.017844

Show Solution