To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as -x^2+ax+bx-5. To find a and b, set up a system to be solved.

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Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. The only such pair is the system solution. displaystylex=-frac32pmfrac12sqrt19 Explanation: displaystyle extusing the method of extcompleting the squaredisplaystyle• ext the coefficient of the x^2 ext term must be 1 ...
3x2+6x-5=0 Two solutions were found : x =(-6-√96)/6=-1-2/3√ 6 = -2.633 x =(-6+√96)/6=-1+2/3√ 6 = 0.633 Step by step solution : Step 1 :Equation at the end of step 1 : (3x2 + 6x) - 5 = 0 ...
4x2+6x-5=0 Two solutions were found : x =(-6-√116)/8=(-3-√ 29 )/4= -2.096 x =(-6+√116)/8=(-3+√ 29 )/4= 0.596 Step by step solution : Step 1 :Equation at the end of step 1 : (22x2 + 6x) - ...
5x2+6x-5=0 Two solutions were found : x =(-6-√136)/10=(-3-√ 34 )/5= -1.766 x =(-6+√136)/10=(-3+√ 34 )/5= 0.566 Step by step solution : Step 1 :Equation at the end of step 1 : (5x2 + 6x) - ...
x2+6x-56=0 Two solutions were found : x =(-6-√260)/2=-3-√ 65 = -11.062 x =(-6+√260)/2=-3+√ 65 = 5.062 Step by step solution : Step 1 :Trying to factor by splitting the middle hatchet ...
More Items     To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as -x^2+ax+bx-5. To find a and b, set up a system to be solved.
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. The only such pair is the system solution.
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, 6 for b, and -5 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 complete the square, the equation must first be in the form x^2+bx=c.
Divide -6, the coefficient of the x term, by 2 to get -3. Then add the square of -3 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
Factor x^2-6x+9. In general, when x^2+bx+c is a perfect square, it can always be factored as left(x+fracb2 ight)^2.

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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 and 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 product of factors rs = C
Two numbers r and s sum up to 6 exactly when the average of the two numbers is frac12*6 = 3. You can also see that the midpoint of r and s corresponds to 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 and s with respect to variable u.  EnglishDeutschEspañolFrançaisItalianoPortuguêsРусский简体中文繁體中文Bahasa MelayuBahasa Indonesiaالعربية日本語TürkçePolskiעבריתČeštinaNederlandsMagyar Nyelv한국어SlovenčinaไทยελληνικάRomânăTiếng Việtहिन्दीঅসমীয়াবাংলাગુજરાતીಕನ್ನಡकोंकणीമലയാളംमराठीଓଡ଼ିଆਪੰਜਾਬੀதமிழ்తెలుగు