Question

Solve each equation by factoring or by using the quadratic formula. The quadratic formula is:

If $a{x}^2+bx+c=0$, with $a\ne 0$, then $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.

$49z^2=1$

Short answer

The values of z are $z=\frac{1}{7}$and $z=-\frac{1}{7}$.

Step-by-step solution

- Understand the concept used 

If $a{x}^2+bx+c=0$, with $a\ne 0$, then $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$. Solving using factoring can be done by splitting the middle term of equation and then making groups and equating them to zero.

- Substitute the values 

It is given that $49z^2=1$which can also be written $49z^2-1=0$.Using quadratic formula $z=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, substitute 49 for a, 0 for b and -1 for c.

Put the values in the formula and get $z=\frac{-\left(0\right)\pm \sqrt{{\left(0\right)}^2-4\times \left(49\right)\times \left(-1\right)}}{2\left(49\right)}$.

- Simplify for z 

Simplify the expression for z.

$\begin{array}{c}z=\frac{-\left(0\right)\pm \sqrt{{\left(0\right)}^2-4\times \left(49\right)\times \left(-1\right)}}{2\left(49\right)}\\ =\frac{0\pm \sqrt{196}}{98}\\ =\frac{\pm \sqrt{196}}{98}\\ =\frac{\pm 14}{98}\end{array}$

Therefore, either $z=\frac{14}{98}$ or $z=\frac{-14}{98}$ that is., either $z=\frac{1}{7}$ or $z=-\frac{1}{7}$.