X 2 X 8 0

$\exponential{(ten)}{2} - 4 10 + eight = 0 $

x=2+2i

x=2-2i

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x^{2}-4x+8=0

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

x=\frac{-\left(-4\correct)±\sqrt{\left(-4\right)^{2}-iv\times 8}}{2}

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -4 for b, and 8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

10=\frac{-\left(-4\right)±\sqrt{16-iv\times viii}}{2}

Square -iv.

x=\frac{-\left(-4\right)±\sqrt{xvi-32}}{2}

Multiply -4 times 8.

x=\frac{-\left(-4\right)±\sqrt{-sixteen}}{2}

Add xvi to -32.

x=\frac{-\left(-iv\correct)±4i}{2}

Have the foursquare root of -16.

x=\frac{4±4i}{two}

The opposite of -4 is four.

x=\frac{iv+4i}{2}

Now solve the equation x=\frac{4±4i}{2} when ± is plus. Add 4 to 4i.

x=\frac{iv-4i}{2}

Now solve the equation 10=\frac{4±4i}{2} when ± is minus. Subtract 4i from iv.

x=2+2i x=2-2i

The equation is now solved.

x^{two}-4x+viii=0

Quadratic equations such as this one can be solved past completing the square. In lodge to complete the square, the equation must get-go exist in the form x^{ii}+bx=c.

x^{2}-4x+8-eight=-8

Subtract 8 from both sides of the equation.

10^{2}-4x=-8

Subtracting viii from itself leaves 0.

10^{2}-4x+\left(-2\right)^{2}=-8+\left(-2\right)^{ii}

Dissever -4, the coefficient of the x term, by 2 to get -2. Then add together the square of -ii to both sides of the equation. This step makes the left mitt side of the equation a perfect square.

x^{2}-4x+4=-eight+4

Square -ii.

x^{2}-4x+four=-4

Add -eight to 4.

\left(x-two\right)^{2}=-4

Factor x^{ii}-4x+4. In full general, when x^{2}+bx+c is a perfect square, information technology tin always be factored equally \left(x+\frac{b}{2}\right)^{ii}.

\sqrt{\left(x-ii\correct)^{2}}=\sqrt{-4}

Accept the foursquare root of both sides of the equation.

10=ii+2i x=2-2i

Add 2 to both sides of the equation.

x ^ ii -4x +eight = 0

Quadratic equations such as this one tin be solved by a new direct factoring method that does not require gauge work. To use the directly factoring method, the equation must be in the form x^2+Bx+C=0.

r + south = 4 rs = 8

Let r and s be the factors for the quadratic equation such that x^ii+Bx+C=(x−r)(x−southward) where sum of factors (r+s)=−B and the production of factors rs = C

r = 2 - u s = two + u

Two numbers r and s sum upwardly to four exactly when the average of the two numbers is \frac{i}{two}*4 = 2. You can also see that the midpoint of r and s corresponds to the centrality of symmetry of the parabola represented past the quadratic equation y=x^2+Bx+C. The values of r and southward are equidistant from the center past an unknown quantity u. Express r and s with respect to variable u. <div style='padding: 8px'><img src='https://opalmath.azureedge.cyberspace/customsolver/quadraticgraph.png' mode='width: 100%;max-width: 700px' /></div>

(2 - u) (ii + u) = eight

To solve for unknown quantity u, substitute these in the production equation rs = 8

four - u^2 = 8

Simplify past expanding (a -b) (a + b) = a^two – b^2

-u^2 = 8-four = 4

Simplify the expression by subtracting 4 on both sides

u^2 = -4 u = \pm\sqrt{-4} = \pm 2i

Simplify the expression by multiplying -1 on both sides and accept the square root to obtain the value of unknown variable u

r =ii - 2i s = 2 + 2i

The factors r and south are the solutions to the quadratic equation. Substitute the value of u to compute the r and s.

X 2 X 8 0,

Source: https://mathsolver.microsoft.com/en/solve-problem/%7B%20x%20%20%7D%5E%7B%202%20%20%7D%20%20-4x%2B8%20%3D%20%200

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