If x^2 + 8x + 5 = 0, which form is correct by completing the square?
Answer and explanation
Correct answer: (x+4)^2 = 11
The governing method is completing the square, which adds the same quantity to both sides so that the quadratic expression becomes a perfect square. Starting with x^2+8x+5=0, move 5 to the right: x^2+8x=-5. Half of the coefficient of x is 8/2=4, and its square is 16. Add 16 to both sides: x^2+8x+16=-5+16=11. The left side factors as (x+4)^2, giving (x+4)^2=11. Thus option A is correct. Option B has the wrong sign because (x-4)^2 produces -8x; option C uses an incorrect square term, and option D omits the required change of 16 on the right-hand side.
Frequently asked questions
What is the correct answer to this question?
(x+4)^2 = 11
Why is this the correct answer?
The governing method is completing the square, which adds the same quantity to both sides so that the quadratic expression becomes a perfect square. Starting with x^2+8x+5=0, move 5 to the right: x^2+8x=-5. Half of the coefficient of x is 8/2=4, and its square is 16. Add 16 to both sides: x^2+8x+16=-5+16=11. The left side factors as (x+4)^2, giving (x+4)^2=11. Thus option A is correct. Option B has the wrong sign because (x-4)^2 produces -8x; option C uses an incorrect square term, and option D omits the required change of 16 on the right-hand side.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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