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How do you solve $x^2-7x=5$ using the quadratic formula?

1 Answer

Aug 8, 2015

$x = (7+sqrt(69))/2$
or
$x = (7-sqrt(69))/2$

Explanation:

Given $x^2-7x =5$

Re-writing in standard form:
$color(white)("XXXX")$ $1x^2-7x-5 = 0$

The general standard form for a quadratic is
$color(white)("XXXX")$ $ax^2+bx+c = 0$

The quadratic formula tells us that the solution for an equation in the general form is:
$color(white)("XXXX")$ $x = (-b+-sqrt(b^2-4ac))/(2a)$

Base on the re-written form of the given equation:
$a=1$ $color(white)("XXXX")$ $b=-7$ $color(white)("XXXX")$ $c=-5$

So the solution is
$color(white)("XXXX")$ $x = (7+-sqrt((-7)^2-4(1)(-5)))/(2(1)$

$color(white)("XXXX")$ $color(white)("XXXX")$ $=(7+-sqrt(69))/2$

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