Q43. - Algebra 1

Question

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

$4x^2+4x=15$

Step-by-Step Solution

Answer

The solutions of the quadratic equations are $\mathbf{-}\frac{\mathbf{5}}{\mathbf{2}}$ and $\frac{\mathbf{3}}{\mathbf{2}}$. 

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 $4x^2+4x=15$. The equation can be rewritten as $4x^2+4x-15=0$. Using the quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, substitute 4 for $a, 4$ for $b$ and $-15$ for $c$.

Put the values in the formula and get $x=\frac{-4\pm \sqrt{{\left(4\right)}^2-4\times \left(4\right)\times \left(-15\right)}}{2\left(4\right)}$. 

Step 3. Write the solutions.

Simplify the expression for $x$.

$x=\frac{-4\pm \sqrt{{\left(4\right)}^2-4\times \left(4\right)\times \left(-15\right)}}{2\left(4\right)}$

  $$\begin{gathered} =\frac{-4\pm \sqrt{16+240}}{8} \\ =\frac{-4\pm 16}{8} \end{gathered}$$ 

Therefore, either

$$\begin{gathered} x=\frac{-4+16}{8} \\ =\frac{3}{2} \end{gathered}$$

or, 

$$\begin{gathered} x=\frac{-4-16}{8} \\ =-\frac{5}{2} \end{gathered}$$ 

that is., either $x=-\frac{5}{2}$ or $x=\frac{3}{2}$.