Solve p^27-1284-111

Question

Simplify the expression

7 p^{2} - 1395

Evaluate

p^{2} \times 7 - 1284 - 111

Use the commutative property to reorder the terms

7 p^{2} - 1284 - 111

Solution

7 p^{2} - 1395

Show Solution

p_{1} = - \frac{3 1085}{7}, p_{2} = \frac{3 1085}{7}

Alternative Form

p_{1} \approx - 14.116859, p_{2} \approx 14.116859

Evaluate

p^{2} \times 7 - 1284 - 111

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

p^{2} \times 7 - 1284 - 111 = 0

Use the commutative property to reorder the terms

7 p^{2} - 1284 - 111 = 0

Subtract the numbers

7 p^{2} - 1395 = 0

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

7 p^{2} = 0 + 1395

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

7 p^{2} = 1395

Divide both sides

\frac{7 p ^{2}}{7} = \frac{1395}{7}

Divide the numbers

p^{2} = \frac{1395}{7}

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

p = \pm \frac{1395}{7}

Simplify the expression

More Steps

Evaluate

\frac{1395}{7}

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

\frac{1395}{7}

Simplify the radical expression

More Steps

Evaluate

1395

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

9 \times 155

Write the number in exponential form with the base of 3

3^{2} \times 155

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

3^{2} \times 155

Reduce the index of the radical and exponent with 2

3155

\frac{3 155}{7}

Multiply by the Conjugate

\frac{3 155 \times 7}{7 \times 7}

Multiply the numbers

More Steps

Evaluate

155 \times 7

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

155 \times 7

Calculate the product

1085

\frac{3 1085}{7 \times 7}

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

\frac{3 1085}{7}

p = \pm \frac{3 1085}{7}

Separate the equation into 2 possible cases

p = \frac{3 1085}{7} p = - \frac{3 1085}{7}

Solution

p_{1} = - \frac{3 1085}{7}, p_{2} = \frac{3 1085}{7}

Alternative Form

p_{1} \approx - 14.116859, p_{2} \approx 14.116859

Show Solution