Solve p^27-1040-14

Question

Simplify the expression

7 p^{2} - 1054

Evaluate

p^{2} \times 7 - 1040 - 14

Use the commutative property to reorder the terms

7 p^{2} - 1040 - 14

Solution

7 p^{2} - 1054

Show Solution

p_{1} = - \frac{7378}{7}, p_{2} = \frac{7378}{7}

Alternative Form

p_{1} \approx - 12.270755, p_{2} \approx 12.270755

Evaluate

p^{2} \times 7 - 1040 - 14

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

p^{2} \times 7 - 1040 - 14 = 0

Use the commutative property to reorder the terms

7 p^{2} - 1040 - 14 = 0

Subtract the numbers

7 p^{2} - 1054 = 0

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

7 p^{2} = 0 + 1054

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

7 p^{2} = 1054

Divide both sides

\frac{7 p ^{2}}{7} = \frac{1054}{7}

Divide the numbers

p^{2} = \frac{1054}{7}

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

p = \pm \frac{1054}{7}

Simplify the expression

More Steps

Evaluate

\frac{1054}{7}

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

\frac{1054}{7}

Multiply by the Conjugate

\frac{1054 \times 7}{7 \times 7}

Multiply the numbers

More Steps

Evaluate

1054 \times 7

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

1054 \times 7

Calculate the product

7378

\frac{7378}{7 \times 7}

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

\frac{7378}{7}

p = \pm \frac{7378}{7}

Separate the equation into 2 possible cases

p = \frac{7378}{7} p = - \frac{7378}{7}

Solution

p_{1} = - \frac{7378}{7}, p_{2} = \frac{7378}{7}

Alternative Form

p_{1} \approx - 12.270755, p_{2} \approx 12.270755

Show Solution