Question

Solve c2-4c3=25 by completing the square

Answer 1

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

What is the completing the square method?

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.

What are the steps justifying the above results?

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:
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