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Use the quadratic formula to solve, 2x^2=7x+6 Leave your answer in simplified radical form.
Please show all your work! (30 points)

Respuesta :

ktreyb
2x² = 7x + 6

Subtract both terms so that we can get 0 on one side. 

2x² - 7x - 6 = 0

Find what factors of - 12 (2 * - 6) add up to be - 7. It's - 4 and - 3. 

2x² - 4x - 3x - 6 = 0
2x(x - 2) - 3(x - 2) = 0
(x - 2)(2x - 3) = 0

Now set each equal to 0.

x - 2 = 0
x = 2

2x - 3 = 0
2x = 3
x = 3/2

x = 3/2, 2
apologiabiology
the quadratic formula can be aplied as follows:
for [tex]ax^2+bx+c=0[/tex], [tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]


given [tex]2x^2=7x+6[/tex]
we need to get it into [tex]ax^2+bx+c=0[/tex] form

minus (7x+6) from both sides
[tex]2x^2-7x-6=0[/tex]
now, a=2, b=-7 c=-6
subsitute
[tex]x=\frac{-(-7) \pm \sqrt{(-7)^2-4(2)(-6)}}{2(2)}[/tex]
[tex]x=\frac{7 \pm \sqrt{49+48}}{4}[/tex]
[tex]x=\frac{7 \pm \sqrt{97}}{4}[/tex]

so [tex]x=\frac{7 + \sqrt{97}}{4}[/tex] or [tex]x=\frac{7 - \sqrt{97}}{4}[/tex]

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