Solve p^2074-60004 - Socratic AI (ScanMath)

Question

Simplify the expression

74 p^{2} - 60004

Evaluate

p^{2} \times 74 - 60004

Solution

74 p^{2} - 60004

Show Solution

2 (37 p^{2} - 30002)

Evaluate

p^{2} \times 74 - 60004

Use the commutative property to reorder the terms

74 p^{2} - 60004

Solution

2 (37 p^{2} - 30002)

Show Solution

p_{1} = - \frac{1110074}{37}, p_{2} = \frac{1110074}{37}

Alternative Form

p_{1} \approx - 28.475689, p_{2} \approx 28.475689

Evaluate

p^{2} \times 74 - 60004

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

p^{2} \times 74 - 60004 = 0

Use the commutative property to reorder the terms

74 p^{2} - 60004 = 0

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

74 p^{2} = 0 + 60004

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

74 p^{2} = 60004

Divide both sides

\frac{74 p ^{2}}{74} = \frac{60004}{74}

Divide the numbers

p^{2} = \frac{60004}{74}

Cancel out the common factor 2

p^{2} = \frac{30002}{37}

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

p = \pm \frac{30002}{37}

Simplify the expression

More Steps

Evaluate

\frac{30002}{37}

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

\frac{30002}{37}

Multiply by the Conjugate

\frac{30002 \times 37}{37 \times 37}

Multiply the numbers

More Steps

Evaluate

30002 \times 37

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

30002 \times 37

Calculate the product

1110074

\frac{1110074}{37 \times 37}

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

\frac{1110074}{37}

p = \pm \frac{1110074}{37}

Separate the equation into 2 possible cases

p = \frac{1110074}{37} p = - \frac{1110074}{37}

Solution

p_{1} = - \frac{1110074}{37}, p_{2} = \frac{1110074}{37}

Alternative Form

p_{1} \approx - 28.475689, p_{2} \approx 28.475689

Show Solution