Question

Solve the following quadratic equation by completing the square: 4r2 + 11x +7=0

Answer 1

Answer:

Step-by-step explanation:

Given the quadratic equation

4r²+11x+7=0

Question is wrong, so let rewrite the question and let it have just one variable, let use x

4x²+11x+7=0

Divide through by 4

4x²/4 + 11x/4 +7/4=0

x²+11x/4 + 7/4=0

x²+11x/4=-7/4

To write the LHS in perfect square, divide the coefficient of x which is 11/4 by 2, after dividing by 2, we will now square the result and add it to both sides of the equations

DIVIDE BY 2=11/4÷2 =11/8

Square=(11/8)²

Then, let add

x²+11x/4 +(11/8)²=-7/4+(11/8)²

Then, the LHS is now a perfect square, so we can weite as

(x+11/8)²=-7/4 +121/64

(x+11/8)²= (-112+121) /64

(x+11/8)²= 9/64

Square root both sides

x+11/8= ±√(9/64)

x= ±√(9/64) - 11/8

Then,

x= ±3/8 - 11/8

So it is either

x=3/8-11/8

x=(3-11)/8

x=-8/8

x=-1

Or

x=-3/8-11/8

x=(-3-11)/8

x=-14/8

x=-7/4

x=-1.75

Then the answer to the quadratic equation using completing the square method is

x=-1 or -1.75