Solve p^27-1027-1

Question

Simplify the expression

7 p^{2} - 1028

Evaluate

p^{2} \times 7 - 1027 - 1

Use the commutative property to reorder the terms

7 p^{2} - 1027 - 1

Solution

7 p^{2} - 1028

Show Solution

p_{1} = - \frac{2 1799}{7}, p_{2} = \frac{2 1799}{7}

Alternative Form

p_{1} \approx - 12.118463, p_{2} \approx 12.118463

Evaluate

p^{2} \times 7 - 1027 - 1

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

p^{2} \times 7 - 1027 - 1 = 0

Use the commutative property to reorder the terms

7 p^{2} - 1027 - 1 = 0

Subtract the numbers

7 p^{2} - 1028 = 0

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

7 p^{2} = 0 + 1028

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

7 p^{2} = 1028

Divide both sides

\frac{7 p ^{2}}{7} = \frac{1028}{7}

Divide the numbers

p^{2} = \frac{1028}{7}

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

p = \pm \frac{1028}{7}

Simplify the expression

More Steps

Evaluate

\frac{1028}{7}

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

\frac{1028}{7}

Simplify the radical expression

More Steps

Evaluate

1028

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

4 \times 257

Write the number in exponential form with the base of 2

2^{2} \times 257

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

2^{2} \times 257

Reduce the index of the radical and exponent with 2

2257

\frac{2 257}{7}

Multiply by the Conjugate

\frac{2 257 \times 7}{7 \times 7}

Multiply the numbers

More Steps

Evaluate

257 \times 7

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

257 \times 7

Calculate the product

1799

\frac{2 1799}{7 \times 7}

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

\frac{2 1799}{7}

p = \pm \frac{2 1799}{7}

Separate the equation into 2 possible cases

p = \frac{2 1799}{7} p = - \frac{2 1799}{7}

Solution

p_{1} = - \frac{2 1799}{7}, p_{2} = \frac{2 1799}{7}

Alternative Form

p_{1} \approx - 12.118463, p_{2} \approx 12.118463

Show Solution