Solve 4^2-4(k-1)(1)<0

$$4 ^ { 2 } - 4 ( k - 1 ) ( 1 ) < 0$$

Solve for k

$$k>5$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$16-4\left(k-1\right)\times 1<0$$

Multiply 4 and 1 to get 4.

$$16-4\left(k-1\right)<0$$

Use the distributive property to multiply -4 by k-1.

$$16-4k+4<0$$

Add 16 and 4 to get 20.

$$20-4k<0$$

Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$-4k<-20$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$k>\frac{-20}{-4}$$

Divide -20 by -4 to get 5.

$$k>5$$