When I solve by completing the square the answer is
Different and when I solve by using the formula ( i.e. x=-b+-√b(squared)-4ac / 2a) the answer is different. Why is that so? It should be same right, no matter which way we solve?
How to solve this equation: 7x(squared) - 20x = 12?
2015-10-08 3:44 pm
回答 (3)
2015-10-08 3:51 pm
Yes, you should get the same answer both ways.
7x² - 20x = 12
divide by the leading coefficient
x² - (20/7)x = 12/7
complete the square
coefficient of the x term: - 20/7
divide coefficient in half: -10/7
square the result: (-10/7)²
add (-10/7)² to both sides:
x² - (20/7)x + (-10/7)² = 12/7 + (-10/7)²
(x - 10/7)² = 84/49 + 100/49 = 184/49
x - 10/7 = ±√(184/49) = ±(2√46)/7
x = 10/7 ± (2√46)/7
Compare to using the quadratic formula:
x = [20 ± √(20² – 4·7(-12))] / [2·7]
= [20 ± √736] / 14
= [20 ± 4√46] /14
= [10 ± 2√46] /7
= 10/7 ± (2√46)/7
7x² - 20x = 12
divide by the leading coefficient
x² - (20/7)x = 12/7
complete the square
coefficient of the x term: - 20/7
divide coefficient in half: -10/7
square the result: (-10/7)²
add (-10/7)² to both sides:
x² - (20/7)x + (-10/7)² = 12/7 + (-10/7)²
(x - 10/7)² = 84/49 + 100/49 = 184/49
x - 10/7 = ±√(184/49) = ±(2√46)/7
x = 10/7 ± (2√46)/7
Compare to using the quadratic formula:
x = [20 ± √(20² – 4·7(-12))] / [2·7]
= [20 ± √736] / 14
= [20 ± 4√46] /14
= [10 ± 2√46] /7
= 10/7 ± (2√46)/7
2015-10-08 4:05 pm
Show your work and your results to learn why you are getting different solutions !!
The solution(s) are the SAME, regardless of your strategy !
7x² - 20x = 12
7x² - 20x - 12 = 0
a = 7, b = - 20, c = - 12
x = [20 ± √(400 + 7 * 48)]/14 = [20 ± √736]/14 = [20 ± 4√46]/14 = [10 ± 2√46] / 7
Show your work for completing the square...I get the same answer when I use that method !!
The solution(s) are the SAME, regardless of your strategy !
7x² - 20x = 12
7x² - 20x - 12 = 0
a = 7, b = - 20, c = - 12
x = [20 ± √(400 + 7 * 48)]/14 = [20 ± √736]/14 = [20 ± 4√46]/14 = [10 ± 2√46] / 7
Show your work for completing the square...I get the same answer when I use that method !!
2015-10-08 4:01 pm
I'll complete the square, and you can compare your version:
7x² - 20x = 12
x² - (20/7)x = 12/7 .... don't forget this step
x² - (20/7)x + (-10/7)² = 12/7 + (10/7)² .... complete the square
(x - 10/7)² = 84/49 + 100/49 = 184/49
x - 10/7 = ±√184 / 7 = ±2√46 / 7
x = (10 ± 2√46) / 7
The quadratic formula gives:
7x² - 20x - 12 = 0 .... put in standard ax² + bx + c = 0 form
x = (20 ± √[(-20)² - 4(7)(-12)]) / 14
= [20 ± √(400 + 336)] / 14 = (20 ± √736) / 14
= (20 ± 4√46) / 14
= (10 ± 2√46) / 7
7x² - 20x = 12
x² - (20/7)x = 12/7 .... don't forget this step
x² - (20/7)x + (-10/7)² = 12/7 + (10/7)² .... complete the square
(x - 10/7)² = 84/49 + 100/49 = 184/49
x - 10/7 = ±√184 / 7 = ±2√46 / 7
x = (10 ± 2√46) / 7
The quadratic formula gives:
7x² - 20x - 12 = 0 .... put in standard ax² + bx + c = 0 form
x = (20 ± √[(-20)² - 4(7)(-12)]) / 14
= [20 ± √(400 + 336)] / 14 = (20 ± √736) / 14
= (20 ± 4√46) / 14
= (10 ± 2√46) / 7
收錄日期: 2021-04-21 14:33:57
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https://hk.answers.yahoo.com/question/index?qid=20151008074404AAZOAoO