How do you solve using the quadratic formula #x^2-3x=-10#?

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Answer 1 · 2018-03-09T03:09:34

See a solution process below:

First, add #color(red)(10)# to each side of the equation to put the equation in standard form:

#x^2 - 3x + color(red)(10) = -10 + color(red)(10)#

#x^2 - 3x + 10 = 0#

We can use the quadratic equation to solve this problem:

For #color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0#, the values of #x# which are the solutions to the equation are given by:

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

Substituting:

#color(red)(1)# for #color(red)(a)#

#color(blue)(-3)# for #color(blue)(b)#

#color(green)(10)# for #color(green)(c)# gives:

#x = (-color(blue)(-3) +- sqrt(color(blue)(-3)^2 - (4 * color(red)(1) * color(green)(10))))/(2 * color(red)(1))#

#x = (3 +- sqrt(9 - 40))/2#

#x = (3 +- sqrt(-31))/2#