Question

10a²-3a=18

Solve for a using the quadratic formula or completing the square.



CAN SOMEONE PLEASE HELP ME

Answer 1

The two solutions are:

$\boxed{a_{1}=\frac{3}{2} \ and \ a_{2}=-\frac{6}{5}}$

Explanation:

Here we have the following equation:

$10a^2-3a=18$

To write this quadratic equation in Standard form, let's subtract 18 from both sides, so:

$10a^2-3a-18=18-18 \\ \\ 10a^2-3a-18=0$

The problem states:

Solve for a using the quadratic formula or completing the square.

So, let's choose the quadratic formula:

$For: \\ \\ ax^2+bx+c=0 \\ \\ \\ The \ quadratic \ formula \ is: \\ \\ x_{12}=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

So:

$a_{12}=\frac{-(-3) \pm \sqrt{(-3)^2-4(10)(-18)}}{2(10)} \\ \\ a_{12}=\frac{3 \pm \sqrt{9+720}}{20} \\ \\ a_{12}=\frac{3 \pm \sqrt{729}}{20} \\ \\ a_{12}=\frac{3 \pm 27}{20} \\ \\ \\ Two \ solutions: \\ \\ a_{1}=\frac{3 + 27}{20} =\frac{30}{20} \therefore \boxed{a_{1}=\frac{3}{2}} \\ \\ \\ a_{2}=\frac{3 - 27}{20} =\frac{-24}{20} \therefore \boxed{a_{2}=-\frac{6}{5}}$

Learn more:

Solving for a variable: https://brainly.com/question/14198414#

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