Question

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

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

Short answer

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

Step-by-step solution

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

role="math" localid="1647851783490" $$\begin{gathered} x=\frac{-5+24.76}{42} \\ =0.47 \end{gathered}$$

or,

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

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