All equations of the size ax^2+bx+c=0 can be solved using the quadratic formula: frac-b±sqrtb^2-4ac2a. The quadratic formula gives two solutions, one when ± is addition và one when it is subtraction.

Bạn đang xem: Solving equations algebraically


This equation is in standard form: ax^2+bx+c=0. Substitute 1 for a, -8 for b, và -12 for c in the quadratic formula, frac-b±sqrtb^2-4ac2a.
*

2x2-8x-12=0 Two solutions were found : x =(4-√40)/2=2-√ 10 = -1.162 x =(4+√40)/2=2+√ 10 = 5.162 Step by step solution : Step 1 :Equation at the kết thúc of step 1 : (2x2 - 8x) - 12 = 0 Step ...
3x2-8x-12=0 Two solutions were found : x =(8-√208)/6=(4-2√ 13 )/3= -1.070 x =(8+√208)/6=(4+2√ 13 )/3= 3.737 Step by step solution : Step 1 :Equation at the over of step 1 : (3x2 - 8x) - 12 ...
4x2-8x-12=0 Two solutions were found : x = 3 x = -1 Step by step solution : Step 1 :Equation at the over of step 1 : (22x2 - 8x) - 12 = 0 Step 2 : Step 3 :Pulling out like terms : ...
9x2-8x-12=0 Two solutions were found : x =(8-√496)/18=(4-2√ 31 )/9= -0.793 x =(8+√496)/18=(4+2√ 31 )/9= 1.682 Step by step solution : Step 1 :Equation at the end of step 1 : (32x2 - 8x) - ...
15x2-8x-12=0 Two solutions were found : x = -2/3 = -0.667 x = 6/5 = 1.200 Step by step solution : Step 1 :Equation at the over of step 1 : ((3•5x2) - 8x) - 12 = 0 Step 2 :Trying lớn ...
-3x2-8x-12=0 Two solutions were found : x =(8-√-80)/-6=4/-3+2i/3√ 5 = -1.3333-1.4907i x =(8+√-80)/-6=4/-3-2i/3√ 5 = -1.3333+1.4907i Step by step solution : Step 1 :Equation at the over of step ...
More Items
*
*

*
*
*

All equations of the form ax^2+bx+c=0 can be solved using the quadratic formula: frac-b±sqrtb^2-4ac2a. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
This equation is in standard form: ax^2+bx+c=0. Substitute 1 for a, -8 for b, và -12 for c in the quadratic formula, frac-b±sqrtb^2-4ac2a.
Quadratic equations such as this one can be solved by completing the square. In order to lớn complete the square, the equation must first be in the form x^2+bx=c.
Divide -8, the coefficient of the x term, by 2 to get -4. Then add the square of -4 lớn both sides of the equation. This step makes the left hand side of the equation a perfect square.
Factor x^2-8x+16. In general, when x^2+bx+c is a perfect square, it can always be factored as left(x+fracb2 ight)^2.

Xem thêm: Công Dụng Bồ Công Anh Có Tác Dụng Gì? Bồ Công Anh Và Câu Chuyện Về Sự Biết Ơn


Quadratic equations such as this one can be solved by a new direct factoring method that does not require guess work. To use the direct factoring method, the equation must be in the form x^2+Bx+C=0.
Let r và s be the factors for the quadratic equation such that x^2+Bx+C=(x−r)(x−s) where sum of factors (r+s)=−B and the sản phẩm of factors rs = C
Two numbers r and s sum up lớn 8 exactly when the average of the two numbers is frac12*8 = 4. You can also see that the midpoint of r and s corresponds khổng lồ the axis of symmetry of the parabola represented by the quadratic equation y=x^2+Bx+C. The values of r and s are equidistant from the center by an unknown quantity u. Express r và s with respect to lớn variable u.
*
*

EnglishDeutschEspañolFrançaisItalianoPortuguêsРусский简体中文繁體中文Bahasa MelayuBahasa Indonesiaالعربية日本語TürkçePolskiעבריתČeštinaNederlandsMagyar Nyelv한국어SlovenčinaไทยελληνικάRomânăTiếng Việtहिन्दीঅসমীয়াবাংলাગુજરાતીಕನ್ನಡकोंकणीമലയാളംमराठीଓଡ଼ିଆਪੰਜਾਬੀதமிழ்తెలుగు