SOLUTION: How do a use the quadratic formula to solve this partial equation.. (4x+1)^2 = 3x+4

Question 245847: How do a use the quadratic formula to solve this partial equation..
(4x+1)^2 = 3x+4
Found 3 solutions by nerdybill, dabanfield, jsmallt9:
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
You would:
- expand the left side
- move all terms to the left
- then apply the quadratic
.
(4x+1)^2 = 3x+4
(4x+1)(4x+1) = 3x+4
16x^2+4x+4x+1 = 3x+4
16x^2+8x+1 = 3x+4
16x^2+5x+1 = 4
16x^2+5x-3 = 0
.
Applying the quadratic yields:
x = {0.3041, -0.6166}
.
Details of quadratic to follow:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=217 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.304091245708007, -0.616591245708007. Here's your graph:

Answer by dabanfield(803)   (Show Source): You can put this solution on YOUR website!
Expand (4x+1)^2 = 16x^2 + 8x + 1
Substutie the above in the original equation:
16x^2 + 8x + 1 = 3x + 4
Collecting terms:
16x^2 + 8x - 3x + 1 - 4 = 0
16x^2 + 5x - 3 = 0
It only remains to substitute a=16, b=8 and c = -3 in the quadratic formula to get the solutions.
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!

To use the quadratic formula, , your equation needs to be in form. So getting the equation into the proper form is where we start.
Multiply out the left side:

Make the right side zero by subtracting 3x and 4 from each side:

Now we have the proper form and we can use the quadratic formula with "a" = 16, "b" = 5 and "c" = -3:

Now we simplify:

So
or
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