All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

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This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -16 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
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4x2-16x-16=0 Two solutions were found : x =(4-√32)/2=2-2√ 2 = -0.828 x =(4+√32)/2=2+2√ 2 = 4.828 Step by step solution : Step 1 :Equation at the end of step 1 : (22x2 - 16x) - 16 = 0 Step ...
2x2-16x-1=0 Two solutions were found : x =(16-√264)/4=4-1/2√ 66 = -0.062 x =(16+√264)/4=4+1/2√ 66 = 8.062 Step by step solution : Step 1 :Equation at the end of step 1 : (2x2 - 16x) - 1 = ...
2x2-16x-6=0 Two solutions were found : x =(8-√76)/2=4-√ 19 = -0.359 x =(8+√76)/2=4+√ 19 = 8.359 Step by step solution : Step 1 :Equation at the end of step 1 : (2x2 - 16x) - 6 = 0 Step ...
2x2-6x-16=0 Two solutions were found : x =(3-√41)/2=-1.702 x =(3+√41)/2= 4.702 Step by step solution : Step 1 :Equation at the end of step 1 : (2x2 - 6x) - 16 = 0 Step 2 : Step 3 ...
3x2-6x-16=0 Two solutions were found : x =(6-√228)/6=1-1/3√ 57 = -1.517 x =(6+√228)/6=1+1/3√ 57 = 3.517 Step by step solution : Step 1 :Equation at the end of step 1 : (3x2 - 6x) - 16 = 0 ...
6x2-16x-6=0 Two solutions were found : x = -1/3 = -0.333 x = 3 Step by step solution : Step 1 :Equation at the end of step 1 : ((2•3x2) - 16x) - 6 = 0 Step 2 : Step 3 :Pulling out like ...
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All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. 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, -16 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
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 -16, the coefficient of the x term, by 2 to get -8. Then add the square of -8 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
Factor x^{2}-16x+64. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{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 16 exactly when the average of the two numbers is \frac{1}{2}*16 = 8. 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.
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