Complete the square for a monic quadratic

Problem

Complete the square for monic quadratic x²+8x+3. Enter half coefficient, square added/subtracted, completion line, vertex form, vertex, and expansion check.

Your answer

A half coefficient=4; square added=16; completion=x²+8x+16−16+3; vertex form=(x+4)²−13; vertex=(-4,-13); expansion check=original B half coefficient=4; square added=16; completion adds 16 but also adds compensation; vertex form=perfect square plus an incorrect constant; vertex has wrong output; expansion check=fails C half coefficient=4; square added=4; completion adds and subtracts 4; vertex form=(x+4)²−1; vertex=(-4,-1); expansion check=fails D half coefficient=4; square added=16; completion correct; vertex form=(x+4)²−13; vertex=(4,-13); expansion check=original

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Complete the square for a monic quadratic

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Hint

Solution walkthrough

Find the completing-square value

Add and subtract that value

Rewrite the perfect square

State the vertex form

Another way

Common mistake