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Quadratic formula is derived from completing the square:
<span>ax² + bx + c = 0 </span>
<span>ax² + bx = −c </span>
<span>x² + b/a x = −c/a </span>
<span>Complete square on left side by adding (b/(2a))² to both sides: </span>
<span>x² + b/a x + (b/(2a))² = (b/(2a))² − c/a </span>
<span>(x + b/(2a))² = (b²−4ac)/(2a)² </span>
<span>x + b/(2a) = ± √(b²−4ac)/(2a) </span>
<span>x = −b/(2a) ± √(b²−4ac)/(2a) </span>
<span>x = (−b ± √(b²−4ac)) / (2a) </span>
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<span>or </span>
<span>ax² + bx + c = 0 </span>
<span>ax² + bx = −c </span>
<span>4a (ax² + bx) = −4ac </span>
<span>4a²x² + 4abx = −4ac </span>
<span>Complete the square on left side by adding b² to both sides </span>
<span>4a²x² + 4abx + b² = b²−4ac </span>
<span>(2ax + b)² = b²−4ac </span>
<span>2ax + b = ± √(b²−4ac) </span>
<span>2ax = −b ± √(b²−4ac) </span>
<span>x = (−b ± √(b²−4ac)) / (2a)</span>
Answer: the number of charms, dollars, 5
I had hard time deciding the attribute.
Step-by-step explanation:
i took the test.