Solve (x+749/2+763)(x+749/2-763)

$$(x+ \frac{ 749 }{ 2 } +763)(x+ \frac{ 749 }{ 2 } -763)$$

Evaluate

$$x^{2}+749x-\frac{1767675}{4}$$

Solution Steps

Convert 763 to fraction \frac{1526}{2}.

$$\left(x+\frac{749}{2}+\frac{1526}{2}\right)\left(x+\frac{749}{2}-763\right)$$

Since \frac{749}{2} and \frac{1526}{2} have the same denominator, add them by adding their numerators.

$$\left(x+\frac{749+1526}{2}\right)\left(x+\frac{749}{2}-763\right)$$

Add 749 and 1526 to get 2275.

$$\left(x+\frac{2275}{2}\right)\left(x+\frac{749}{2}-763\right)$$

Convert 763 to fraction \frac{1526}{2}.

$$\left(x+\frac{2275}{2}\right)\left(x+\frac{749}{2}-\frac{1526}{2}\right)$$

Since \frac{749}{2} and \frac{1526}{2} have the same denominator, subtract them by subtracting their numerators.

$$\left(x+\frac{2275}{2}\right)\left(x+\frac{749-1526}{2}\right)$$

Subtract 1526 from 749 to get -777.

$$\left(x+\frac{2275}{2}\right)\left(x-\frac{777}{2}\right)$$

Apply the distributive property by multiplying each term of x+\frac{2275}{2} by each term of x-\frac{777}{2}.

$$x^{2}+x\left(-\frac{777}{2}\right)+\frac{2275}{2}x+\frac{2275}{2}\left(-\frac{777}{2}\right)$$

Combine x\left(-\frac{777}{2}\right) and \frac{2275}{2}x to get 749x.

$$x^{2}+749x+\frac{2275}{2}\left(-\frac{777}{2}\right)$$

Multiply \frac{2275}{2} times -\frac{777}{2} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}+749x+\frac{2275\left(-777\right)}{2\times 2}$$

Do the multiplications in the fraction \frac{2275\left(-777\right)}{2\times 2}.

$$x^{2}+749x+\frac{-1767675}{4}$$

Fraction \frac{-1767675}{4} can be rewritten as -\frac{1767675}{4} by extracting the negative sign.

$$x^{2}+749x-\frac{1767675}{4}$$

Expand

$$x^{2}+749x-\frac{1767675}{4}$$

Solution Steps

Convert 763 to fraction \frac{1526}{2}.

$$\left(x+\frac{749}{2}+\frac{1526}{2}\right)\left(x+\frac{749}{2}-763\right)$$

Since \frac{749}{2} and \frac{1526}{2} have the same denominator, add them by adding their numerators.

$$\left(x+\frac{749+1526}{2}\right)\left(x+\frac{749}{2}-763\right)$$

Add 749 and 1526 to get 2275.

$$\left(x+\frac{2275}{2}\right)\left(x+\frac{749}{2}-763\right)$$

Convert 763 to fraction \frac{1526}{2}.

$$\left(x+\frac{2275}{2}\right)\left(x+\frac{749}{2}-\frac{1526}{2}\right)$$

Since \frac{749}{2} and \frac{1526}{2} have the same denominator, subtract them by subtracting their numerators.

$$\left(x+\frac{2275}{2}\right)\left(x+\frac{749-1526}{2}\right)$$

Subtract 1526 from 749 to get -777.

$$\left(x+\frac{2275}{2}\right)\left(x-\frac{777}{2}\right)$$

Apply the distributive property by multiplying each term of x+\frac{2275}{2} by each term of x-\frac{777}{2}.

$$x^{2}+x\left(-\frac{777}{2}\right)+\frac{2275}{2}x+\frac{2275}{2}\left(-\frac{777}{2}\right)$$

Combine x\left(-\frac{777}{2}\right) and \frac{2275}{2}x to get 749x.

$$x^{2}+749x+\frac{2275}{2}\left(-\frac{777}{2}\right)$$

Multiply \frac{2275}{2} times -\frac{777}{2} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}+749x+\frac{2275\left(-777\right)}{2\times 2}$$

Do the multiplications in the fraction \frac{2275\left(-777\right)}{2\times 2}.

$$x^{2}+749x+\frac{-1767675}{4}$$

Fraction \frac{-1767675}{4} can be rewritten as -\frac{1767675}{4} by extracting the negative sign.

$$x^{2}+749x-\frac{1767675}{4}$$