How do you solve $x^{2} = 12 x - 27$ $x^2=12x-27$ ?

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How do you solve $x^{2} = 12 x - 27$ $x^2=12x-27$ ?

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Answer 1 · 2015-05-23T09:49:46

$x^{2} = 12 x - 27$ $x^2=12x-27$
$x^{2} - 12 x + 27 = 0$ $x^2 -12x+27=0$

We can Split the Middle Term of this expression to factorise it and thereby find the solution.
In this technique, if we have to factorise an expression like $a x^{2} + b x + c$ $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_{1} \cdot N_{2} = a \cdot c = 1 \cdot 27 = 27$ $N_1*N_2 = a*c = 1*27 = 27$
And
N_1 +N_2 = b = -12#

After trying out a few numbers we get $N_{1} = - 9$ $N_1 = -9$ and $N_{2} = - 3$ $N_2 =-3$
$9 \cdot 3 = 27$ $9*3 = 27$ , and $- 9 + (- 3) = - 12$ $-9+(-3)= -12$

$x^{2} - 12 x + 27 = x^{2} - 9 x - 3 x + 27$ $x^2 -12x+27= x^2 -9x - 3x +27$
$x (x - 9) - 3 (x - 9) = 0$ $x(x - 9) - 3(x-9) = 0$

$(x - 9) (x - 3)$ $color(green)((x-9)(x - 3)$ is the factorised form.
and $x = 9 and x = 3$ $color(green)(x=9 and x=3$ are the solutions.

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How do you solve $x^{2} = 12 x - 27$ $x^2=12x-27$ ?

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