Q39. - Algebra 1

Question

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.

$21x^2+5x-7=0$

Step-by-Step Solution

Answer

The solutions of the quadratic equations are 0.47 and $\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{71}$. 

Step 1. 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 the equation and then making groups and equating them to zero.

Step 2. Substitute the values .

It is given that $21x^2+5x-7=0$. Using the quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, substitute 21 for $a, 5$ for b and $-7$ for $c$.

Put the values in the formula and get $x=\frac{-5\pm \sqrt{{\left(5\right)}^2-4\times \left(21\right)\times \left(-7\right)}}{2\left(21\right)}$. 

Step 3. Write the solutions.

Simplify the expression for $x$.

 $x=\frac{-5\pm \sqrt{{\left(5\right)}^2-4\times \left(21\right)\times \left(-7\right)}}{2\left(21\right)}$

   $$\begin{gathered} =\frac{-5\pm \sqrt{25+588}}{42} \\ =\frac{-5\pm \sqrt{613}}{42} \\ =\frac{-5\pm 24.76}{42} \end{gathered}$$

Therefore, either

  $$\begin{gathered} x=\frac{-5+24.76}{42} \\ =0.47 \end{gathered}$$

or, 

$$\begin{gathered} x=\frac{-5-24.76}{42} \\ =-0.71 \end{gathered}$$

that is., either $x=0.47$ or $x=-0.71$.