Q16. - Algebra 1

Question

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

$x^2-10x=-15$

Step-by-Step Solution

Answer

The solutions of the quadratic equations are 8.2 and 1.8.

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 equation and then making groups and equating them to zero.

Step 2. Substitute the values .

It is given that $x^2-10x=-15$. The equation can be rewritten as $x^2-10x+15=0$. Using quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, substitute 1 for $a, -10$ for b and 15 for c. 

Put the values in the formula and get $x=\frac{-\left(-10\right)\pm \sqrt{{\left(-10\right)}^2-4\times \left(1\right)\times \left(15\right)}}{2\left(1\right)}$.

Step 3. Write the solutions.

Simplify the expression for x.

$$\begin{gathered} x=\frac{-\left(-10\right)\pm \sqrt{{\left(-10\right)}^2-4\times \left(1\right)\times \left(15\right)}}{2\left(1\right)} \\ =\frac{10\pm \sqrt{100-60}}{2} \\ =\frac{10\pm 2\sqrt{10}}{2} \\ =5\pm \sqrt{10} \end{gathered}$$ 

 

Therefore, either

$$\begin{gathered} x=5+\sqrt{10} \\ =8.2 \end{gathered}$$ 

 

or, 

 

$$\begin{gathered} x=5-\sqrt{10} \\ =1.8 \end{gathered}$$ 

that is., either $x=8.2$ or $x=1.8$.