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Given the function y = x2 + 2x - 8, what are the values of x when y = 3?

Sagot :

Answer:

[tex]x = - 1 + 2 \sqrt{3} [/tex]

[tex]x = - 1 - 2 \sqrt{3} [/tex]

Step-by-step explanation:

[tex] {x}^{2} + 2x - 8= 3[/tex]

[tex] {x}^{2} + 2x = 11[/tex]

Complete the square

[tex] (\frac{2}{2} ) {}^{2} = 1[/tex]

so

[tex] {x}^{2} + 2x + 1 = 11 + 1[/tex]

[tex] {x}^{2} + 2x + 1 = 12[/tex]

[tex]( x + 1) {}^{2} = 12[/tex]

[tex]x + 1 = \sqrt{12} [/tex]

[tex]x = - 1 + \sqrt{12} [/tex]

or

[tex]x + 1 = - \sqrt{12} [/tex]

[tex]x = - 1 - \sqrt{12} [/tex]

If you want it simplified, you could say

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