Having solved by the Completing the Square method, c is given as:
c= ± [√229/3] + 2/3 or in decimal form:
c = 5.71091531; -4.37758198
<h3>What is the completing the square method?</h3>
One way for locating the roots of a quadratic equation is to complete the square method.
We must turn the provided equation into a perfect square using this approach.
The quadratic formula may also be used to get the roots of a quadratic problem.
<h3>What are the steps justifying the above results?</h3>
Step 1: First re-arrange all nonzero terms to the left side of the equation:
c² - (4c/3) - 25 = 0
Step 2: Identify the Coefficients:
a = 1;
b= -4/3
c = -25
Let us move -25 to the right-hand side:
x² - 1.33x = 25
Now, take divide the coefficient of x by 2 and square it:
(-1.33/2)2 = -0.6652 = 0.44
Add this number to both sides of the equation:
x² - 1.33x + 0.44 = 25 + 0.44
Let us simplify the right-hand side:
x² - 1.33x + 0.44 = 25.44
After some slight rewriting:
x² - 2*0.665x + 0.44 = 25.44
To the left hand-side we apply the formula:
p2 - 2pq + q2=(p - q)2
with p = x and q = 0.665:
(x - 0.665)2 = 25.44
Take the square root of both sides:
x - 0.665 = ± √25.44
and so
x = 0.665 ± √25.44
which gives
x = 0.665 ±5.04
Finally, we have
c = 5.71091531; or -4.37758198
Learn more about completing the square:
brainly.com/question/13981588
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