SOLUTION: x squared-8x-29=(this equal sign has 3 lines)(x+a)squared+b, where a and b are constants. find the value of a and the value of b
Algebra.Com
Question 352786: x squared-8x-29=(this equal sign has 3 lines)(x+a)squared+b, where a and b are constants. find the value of a and the value of b
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
^2\ +\ b)
This is a "Complete the Square" problem.
Start by setting the LHS equal to zero.
Add the opposite of the constant term to both sides:
Divide the coefficient on the first degree term by 2, square the result, and then add that result to both sides. -8 divided by 2 is -4. -4 squared is 16. Add 16 to both sides:
The quadradic trinomial in the LHS is now a perfect square. Factor it:
^2\ =\ 45)
Add the opposite of the constant term to both sides:
^2\ -\ 45\ =\ 0)
Since both the original LHS and this new LHS are equal to zero, they must be equivalent, hence:
)^2\ +\ (-45))
But the original LHS was equivalent to ^2\ +\ b)
, hence:
^2\ +\ b\ \equiv\ (x\ +\ (-4))^2\ +\ (-45))
Therefore:
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
if a squared + b squared=11 and ab=3 find the value of... (answered by psbhowmick)
if a squared minus b squared is equal to 8 and a minus b is equal to 2 ,find the value of (answered by rothauserc)
An equation has the form {{{(a/x)+(x/b)=c}}}, where a, b and c are... (answered by josgarithmetic)
Equation (x+2)(x+a)=x^2 + 4x+b where a and b are constants. If the equation is true for... (answered by ikleyn)
When the polynomial F(x) of degree 3 is divided by x-1,the remainder is -1.When F(x) is... (answered by ikleyn)
Find the value of the constants A, B, C and D in the following identity:
{{{... (answered by Fombitz)
can you please help me with this problem because i keep getting stuck on it and i can't... (answered by checkley71)
If a and b are constants, where is the zero of the function?
{{{y = (x + a)/(x + b)... (answered by jim_thompson5910)
The equation x²+ px +4 = 0, where p and q are constants, has roots -1 and 4. a) Find the (answered by greenestamps,MathLover1,ikleyn)
