Question

Solve the quadratic using the quadratic formula 02%20%3D%200" id="TexFormula1" title="5x {}^{2} + 12x - 2 = 0" alt="5x {}^{2} + 12x - 2 = 0" align="absmiddle" class="latex-formula">

Answer 1

The quadratic formula:

$ax^2+bx+c=0\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a};\ x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}$

We have:

$5x^2+12x-2=0\\\\a=5;\ b=12;\ c=-2\\\\b^2-4ac=12^2-4\cdot5\cdot(-2)=144+40=184\\\\\sqrt{b^2-4ac}=\sqrt{184}=\sqrt{4\cdot46}=2\sqrt{46}$

substitute

$x_1=\dfrac{-12-2\sqrt{46}}{2\cdot5}=\dfrac{-6-\sqrt{46}}{5}\\\\x_2=\dfrac{-12+2\sqrt{46}}{2\cdot5}=\dfrac{-6+\sqrt{46}}{5}$