How do you solve #10x^2=-7x+6# using the quadratic formula?

1 Answer
R. Nguyen
Mar 11, 2018

#x = 1/2# or #x = -6/5#

Explanation:

The quadratic formula allows us to find the value of #x# for an equation in the form #ax^2 + bx + c = 0# where #a ne 0#. In the case that the equation is in this form:

#x = (-color(green)b +- sqrt(color(green)b^2 - 4color(red)acolor(blue)c))/(2color(red)a)#

The first thing we notice is that this equation is not in that form, so we should rearrange the terms so it is.

#10x^2 = -7x + 6#

#color(red)10x^2 + color(green)7x color(blue)(- 6) = 0#

Now, we can substitute our coefficients into the quadratic formula. I recommend using parentheses around each coefficient to help ensure all of the signs are correct in our final answer.

#x = (-(color(green)7) +- sqrt((color(green)7)^2 - 4(color(red)10)(color(blue)(-6))))/(2(color(red)10))#

#x = (-7 +- sqrt(289))/20#

#x = (-7 +- 17)/20#

#x = (-7 + 17)/20# or #x = (-7 - 17)/20#

#x = 10/20# or #x = (-24)/20#

#x = 1/2# or #x = -6/5#

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