Solve b^22-17001 - ScanMath

Question

Simplify the expression

2 b^{2} - 17001

Evaluate

b^{2} \times 2 - 17001

Solution

2 b^{2} - 17001

Show Solution

b_{1} = - \frac{3 3778}{2}, b_{2} = \frac{3 3778}{2}

Alternative Form

b_{1} \approx - 92.198156, b_{2} \approx 92.198156

Evaluate

b^{2} \times 2 - 17001

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

b^{2} \times 2 - 17001 = 0

Use the commutative property to reorder the terms

2 b^{2} - 17001 = 0

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

2 b^{2} = 0 + 17001

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

2 b^{2} = 17001

Divide both sides

\frac{2 b ^{2}}{2} = \frac{17001}{2}

Divide the numbers

b^{2} = \frac{17001}{2}

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

b = \pm \frac{17001}{2}

Simplify the expression

More Steps

Evaluate

\frac{17001}{2}

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

\frac{17001}{2}

Simplify the radical expression

More Steps

Evaluate

17001

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

9 \times 1889

Write the number in exponential form with the base of 3

3^{2} \times 1889

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

3^{2} \times 1889

Reduce the index of the radical and exponent with 2

31889

\frac{3 1889}{2}

Multiply by the Conjugate

\frac{3 1889 \times 2}{2 \times 2}

Multiply the numbers

More Steps

Evaluate

1889 \times 2

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

1889 \times 2

Calculate the product

3778

\frac{3 3778}{2 \times 2}

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

\frac{3 3778}{2}

b = \pm \frac{3 3778}{2}

Separate the equation into 2 possible cases

b = \frac{3 3778}{2} b = - \frac{3 3778}{2}

Solution

b_{1} = - \frac{3 3778}{2}, b_{2} = \frac{3 3778}{2}

Alternative Form

b_{1} \approx - 92.198156, b_{2} \approx 92.198156

Show Solution