Question

Explain how to solve 5x2-3x=25 by completing the square. What are the solutions

Answer 1

5x2-3x=25

Divide each term by 5:

x^2 - 3/5x = 5

Make a trinomial square of the left side by taking the square of half of the coefficient of x.

The coefficient of x is -3, so the square would be (-3/10)^2

Add that to both sides of the equation.

Now you have:

x^2 - 3/5x + (-3/10)^2 = 5 + (-3/10)^2

Simplify both sides:

x^2 -3/5x +9/100 = 509/100

Factor the trinomial:

(x-3/10)^2 = 509/100

Solve for x, , take the square root of both sides:

x-3/10 = +/-√509 / 100

Simplify the right side:

x-3/10 = +/-√509/10

Add 3/10 to both sides:

X = +/-√509/10 + 3/10 ( this is the exact form)

You can then find the decimal answer if needed.