SOLUTION: how do you solve quadratic equations and then also simplify the radical solution??? examle: 5(x.squared)- (x.squared)=42 help!!!

Question 83944: how do you solve quadratic equations and then also simplify the radical solution???
examle: 5(x.squared)- (x.squared)=42

help!!!
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
If you want, you can solve this without using the quadratic formula. Notice that the left
side of this equation simplifies to:
.

.
So you can substitute for the left side of the equation you were given. This
makes the given equation become:
.

.
Then you can find by dividing both sides by 4 which is the multiplier of the
term. This division of both sides by 4 reduces the equation to:
.

.
and
.
Substituting for results in the equation becoming:
.

.
and taking the square root of both sides gives you the two answers:
.
and
.
And since the square root of 10.5 is (from a calculator) 3.240370349, the two answers to
this problem are:
.
and
.
But if you have to do the problem using the quadratic formula, you need to get the
original problem into the standard quadratic form of:
.

.
You still combine the two terms on the left side of the original equation to get:
.

.
just as we did above. Next you need to get zero on the right side as the standard
quadratic form calls for. Do this by subtracting 42 from both sides of the equation.
That subtraction results in:
.

.
This is in the standard quadratic form in which a = 4, b = 0 (because there is no term
that contains just x), and c = -42.
.
The quadratic formula says that the answer to the problem is determined by the equation:
.

.
Since b = 0 in this problem, the equation reduces to:
.

.
Next substitute 4 for a and -42 for c to get:
.

.
The term in the radical [that is -4*4*(-42)] multiplies out to be 672 so the problem becomes:
.

.
The denominator of (2*4) becomes 8 which further simplifies the problem to:
.

.
Since the square root of 672 is (by a calculator) 25.92296279 the answers to this
problem become:
.
and
.
When you do the division, the two answers are:
.
and
.
And these are the same answers that we found earlier without using the quadratic formula.
.
Hope this discussion helps you to work your way through the problem.
RELATED QUESTIONS
I need to solve these quadratic equations using the method that came from India. I am... (answered by solver91311)

how do you do the quadratic formula and solve for x squared + 7x -... (answered by stanbon,Alan3354)

how do you simplify radical 8x... (answered by lwsshak3)

I am in 9th grade and taking Algebra 1. We are now learning to solve quadratic equations... (answered by ilana)

how do you solve this system of equations x squared + y squared = 9... (answered by funmath)

can you show me how to solve? Simplify and show the restrictions: x Squared -5x divided... (answered by ikleyn)

how do you solve the quadratic equation x squared -9x-10=0 by... (answered by user_dude2008)

How do I solve equations quadratic equations like this? 4 and then x under a radical... (answered by MathLover1,solver91311)

how do you solve x squared + 10x + 25 all under a... (answered by persian52)