Solve B=(4x-7)(1+x)+1+2x+x^2

$$B = ( 4 x - 7 ) ( 1 + x ) + 1 + 2 x + x ^ { 2 }$$

Solve for B

$$B=-\left(6+x-5x^{2}\right)$$

Solution Steps

Use the distributive property to multiply 4x-7 by 1+x and combine like terms.

$$B=-3x+4x^{2}-7+1+2x+x^{2}$$

Add -7 and 1 to get -6.

$$B=-3x+4x^{2}-6+2x+x^{2}$$

Combine -3x and 2x to get -x.

$$B=-x+4x^{2}-6+x^{2}$$

Combine 4x^{2} and x^{2} to get 5x^{2}.

$$B=-x+5x^{2}-6$$

Solve for x (complex solution)

$$x=\frac{\sqrt{20B+121}+1}{10}$$

$$x=\frac{-\sqrt{20B+121}+1}{10}$$

Solve for x

$$x=\frac{\sqrt{20B+121}+1}{10}$$

$$x=\frac{-\sqrt{20B+121}+1}{10}\text{, }B\geq -\frac{121}{20}$$