Solve p^2812-69005

Question

Simplify the expression

812 p^{2} - 69005

Evaluate

p^{2} \times 812 - 69005

Solution

812 p^{2} - 69005

Show Solution

p_{1} = - \frac{14008015}{406}, p_{2} = \frac{14008015}{406}

Alternative Form

p_{1} \approx - 9.218543, p_{2} \approx 9.218543

Evaluate

p^{2} \times 812 - 69005

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

p^{2} \times 812 - 69005 = 0

Use the commutative property to reorder the terms

812 p^{2} - 69005 = 0

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

812 p^{2} = 0 + 69005

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

812 p^{2} = 69005

Divide both sides

\frac{812 p ^{2}}{812} = \frac{69005}{812}

Divide the numbers

p^{2} = \frac{69005}{812}

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

p = \pm \frac{69005}{812}

Simplify the expression

More Steps

Evaluate

\frac{69005}{812}

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

\frac{69005}{812}

Simplify the radical expression

More Steps

Evaluate

812

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

4 \times 203

Write the number in exponential form with the base of 2

2^{2} \times 203

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

2^{2} \times 203

Reduce the index of the radical and exponent with 2

2203

\frac{69005}{2 203}

Multiply by the Conjugate

\frac{69005 \times 203}{2 203 \times 203}

Multiply the numbers

More Steps

Evaluate

69005 \times 203

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

69005 \times 203

Calculate the product

14008015

\frac{14008015}{2 203 \times 203}

Multiply the numbers

More Steps

Evaluate

2203 \times 203

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

2 \times 203

Multiply the terms

406

\frac{14008015}{406}

p = \pm \frac{14008015}{406}

Separate the equation into 2 possible cases

p = \frac{14008015}{406} p = - \frac{14008015}{406}

Solution

p_{1} = - \frac{14008015}{406}, p_{2} = \frac{14008015}{406}

Alternative Form

p_{1} \approx - 9.218543, p_{2} \approx 9.218543

Show Solution