Question 395154
The solution provided by another tutor does not use the Quadratic Formula as the problem specifies and there is a typographics error in the first solution.<br>
question 1 : {{{2a^2-46a+252=0}}}
Dividing both sides by 2 will make the "a", "b" and "c" smaller. This will make the rest of the problem easier:
{{{a^2-23a+126=0}}}
The Quadratic Formula:
{{{x = (-(-23) +- sqrt((-23)^2 - 4(1)(126)))/2(1)}}}
which simplifies as follows:
{{{x = (23 +- sqrt(529 - 504))/2}}}
{{{x = (23 +- sqrt(25))/2}}}
{{{x = (23 +- 5)/2}}}
In long form this is:
{{{x = (23 + 5)/2}}} or {{{x = (23 - 5)/2}}}
{{{x = 28/2}}} or {{{x = 18/2}}}
x = 14 or x = 9<br>
question 2 : {{{x^2-4x=5}}}
One side needs to be zero so we start by subtracting 5 from each side:
{{{x^2-4x-5=0}}}
The Quadratic Formula:
{{{x = (-(-4) +- sqrt((-4)^2 - 4(1)(-5)))/2(1)}}}
which simplifies as follows:
{{{x = (4 +- sqrt(16 - 4(1)(-5)))/2}}}
{{{x = (4 +- sqrt(16 + 20))/2}}}
{{{x = (4 +- sqrt(36))/2}}}
{{{x = (4 +- 6)/2}}}
In long form this is:
{{{x = (4 + 6)/2}}} or {{{x = (4 - 6)/2}}}
{{{x = 10/2}}} or {{{x = (-2)/2}}}
x = 5 or x = -1