Solve N=-3x(5-2x)-(-4x)^2+2(-7x)

$$N = - 3 x ( 5 - 2 x ) - ( - 4 x ) ^ { 2 } + 2 ( - 7 x )$$

Solve for N

$$N=-x\left(10x+29\right)$$

Solution Steps

Use the distributive property to multiply -3x by 5-2x.

$$N=-15x+6x^{2}-\left(-4x\right)^{2}+2\left(-7\right)x$$

Expand \left(-4x\right)^{2}.

$$N=-15x+6x^{2}-\left(-4\right)^{2}x^{2}+2\left(-7\right)x$$

Calculate -4 to the power of 2 and get 16.

$$N=-15x+6x^{2}-16x^{2}+2\left(-7\right)x$$

Combine 6x^{2} and -16x^{2} to get -10x^{2}.

$$N=-15x-10x^{2}+2\left(-7\right)x$$

Multiply 2 and -7 to get -14.

$$N=-15x-10x^{2}-14x$$

Combine -15x and -14x to get -29x.

$$N=-29x-10x^{2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{841-40N}-29}{20}$$

$$x=\frac{-\sqrt{841-40N}-29}{20}$$

Solve for x

$$x=\frac{\sqrt{841-40N}-29}{20}$$

$$x=\frac{-\sqrt{841-40N}-29}{20}\text{, }N\leq \frac{841}{40}$$