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Sagot :

Kidpreneur

Answer:

[tex](X+10)^2 = 106[/tex]

Step-by-step explanation:

To convert the quadratic equation [tex]X^2+20x-6=0[/tex] into the form [tex](x-p)^2=q[/tex], we need to complete the square. Let's go through this step-by-step:

First, let's start with our equation:

[tex]X^2+20x-6=0[/tex]

Move the constant term to the right side of the equation:

[tex]X^2+20x = 6[/tex]

To complete the square, we take half of the coefficient of x, square it, and add and subtract it from both sides:

Half of 20 is 10, and [tex]10^2 = 100[/tex]

[tex]X^2+20x+100 = 6+100[/tex]

Simplify the right side:

[tex]X^2+20x+100 = 106[/tex]

The left side is now a perfect square trinomial:

[tex](X+10)^2 = 106[/tex]

This is almost in[tex](x-p)^2=q[/tex] form. We just need to adjust it slightly:

[tex](X-(-10))^2 = 106[/tex]

Therefore, in [tex](x-p)^2=q[/tex] form, the equation [tex]X^2+20x-6=0[/tex] becomes:

[tex](X+10)^2 = 106[/tex]

Where [tex]p = -10[/tex]  and [tex]q = 106[/tex]

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