Solve b^2442-51714

Question

Simplify the expression

442 b^{2} - 51714

Evaluate

b^{2} \times 442 - 51714

Solution

442 b^{2} - 51714

Show Solution

442 (b^{2} - 117)

Evaluate

b^{2} \times 442 - 51714

Use the commutative property to reorder the terms

442 b^{2} - 51714

Solution

442 (b^{2} - 117)

Show Solution

b_{1} = - 313, b_{2} = 313

Alternative Form

b_{1} \approx - 10.816654, b_{2} \approx 10.816654

Evaluate

b^{2} \times 442 - 51714

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

b^{2} \times 442 - 51714 = 0

Use the commutative property to reorder the terms

442 b^{2} - 51714 = 0

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

442 b^{2} = 0 + 51714

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

442 b^{2} = 51714

Divide both sides

\frac{442 b ^{2}}{442} = \frac{51714}{442}

Divide the numbers

b^{2} = \frac{51714}{442}

Divide the numbers

More Steps

Evaluate

\frac{51714}{442}

Reduce the numbers

\frac{117}{1}

Calculate

117

b^{2} = 117

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

b = \pm 117

Simplify the expression

More Steps

Evaluate

117

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

9 \times 13

Write the number in exponential form with the base of 3

3^{2} \times 13

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

3^{2} \times 13

Reduce the index of the radical and exponent with 2

313

b = \pm 313

Separate the equation into 2 possible cases

b = 313 b = - 313

Solution

b_{1} = - 313, b_{2} = 313

Alternative Form

b_{1} \approx - 10.816654, b_{2} \approx 10.816654

Show Solution