to lớn solve the equation, factor x^2-4x-5 using formula x^2+left(a+b ight)x+ab=left(x+a ight)left(x+b ight). To lớn find a và b, phối up a system lớn be solved.

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Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. The only such pair is the system solution.
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Dean R. Apr 25, 2018displaystyle0=left(x^2-4x ight)-5=left(x^2-4x+4 ight)-4-5=left(x-2 ight)^2-9quadso displaystyleleft(x-2 ight)^2=9quad extorquadx-2=pmsqrt9quad extorquadx=2pm3 ...
2x2-4x-5=0 Two solutions were found : x =(4-√56)/4=1-1/2√ 14 = -0.871 x =(4+√56)/4=1+1/2√ 14 = 2.871 Step by step solution : Step 1 :Equation at the end of step 1 : (2x2 - 4x) - 5 = 0 ...
(3x2)-4x-5=0 Two solutions were found : x =(4-√76)/6=(2-√ 19 )/3= -0.786 x =(4+√76)/6=(2+√ 19 )/3= 2.120 Step by step solution : Step 1 :Equation at the over of step 1 : (3x2 - 4x) - 5 = 0 ...
4x2-4x-5=0 Two solutions were found : x =(4-√96)/8=(1-√ 6 )/2= -0.725 x =(4+√96)/8=(1+√ 6 )/2= 1.725 Step by step solution : Step 1 :Equation at the over of step 1 : (22x2 - 4x) - 5 = 0 ...
5x2-4x-5=0 Two solutions were found : x =(4-√116)/10=(2-√ 29 )/5= -0.677 x =(4+√116)/10=(2+√ 29 )/5= 1.477 Step by step solution : Step 1 :Equation at the end of step 1 : (5x2 - 4x) - 5 = ...
6x2-4x-5=0 Two solutions were found : x =(4-√136)/12=1/3-1/6√ 34 = -0.638 x =(4+√136)/12=1/3+1/6√ 34 = 1.305 Step by step solution : Step 1 :Equation at the end of step 1 : ((2•3x2) - 4x) ...
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To solve the equation, factor x^2-4x-5 using formula x^2+left(a+b ight)x+ab=left(x+a ight)left(x+b ight). To find a và b, set up a system khổng lồ be solved.
Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. The only such pair is the system solution.
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 lớn find a và b, set up a system lớn be solved.
Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. The only such pair is the system solution.
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.
This equation is in standard form: ax^2+bx+c=0. Substitute 1 for a, -4 for b, & -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 khổng lồ complete the square, the equation must first be in the size x^2+bx=c.
Divide -4, the coefficient of the x term, by 2 lớn get -2. Then địa chỉ cửa hàng the square of -2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
Factor x^2-4x+4. 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. Lớn use the direct factoring method, the equation must be in the khung 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 hàng hóa of factors rs = C
Two numbers r và s sum up khổng lồ 4 exactly when the average of the two numbers is frac12*4 = 2. You can also see that the midpoint of r và 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 and s with respect to lớn variable u.
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