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3 years ago

Solve 2x2 – 6x + 10 = 0 by completing the square.

Mathematics

1 answer:

astraxan [27]3 years ago

4 0

Answer: x = 6.32 or -0.32

Step-by-step explanation:

2x² - 6x + 10 = 0

No we divide the expression by 2 to make the coefficient of x² equals 1

We now have

x² - 3x + 5 = 0

Now we remove 5 to the other side of the equation

x² - 3x = -5

we add to both side square of half the coefficient of x which is 3

x² - 3x + ( ⁻³/₂)² = -5 + (⁻³/₂)²

(x - ³/₂)² = -5 + ⁹/₄

Resolve into fraction

(x - ³/₂)² = ⁻¹¹/4

Take the roots of the equation

x - ³/₂ = √¹¹/₄

x - ³/₂ = √11/₂

x = ³/₂ ± 3.32/₂

= 3+ 3.32 or 3 - 3.32

= 6.32 or - 0.32

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$\quad \huge \quad \quad \boxed{ \tt \:Answer }$

$\qquad \tt \rightarrow \:Domain = [-9, -1]$

$\qquad \tt \rightarrow \:Range = [-1 , 3]$

____________________________________

$\large \tt Solution \: :$

Domain = All possible values of x for which f(x) is defined

[ generally the extension of function in x - direction ]

Range = All possible values of f(x)

[ generally the extension of function in y - direction ]

$\large\textsf{For the given graph : }$

$\qquad \tt \rightarrow \: domain = [ - 9, -1]$

$\qquad \tt \rightarrow \: range= [ -1,3]$

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