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Solve the following quadratic equatikns by the factor method. Show your solution.
[tex]1.x { }^{2} = 2x[/tex]
[tex]2.x(x + 1) = 12[/tex]
[tex]3.x(x + 1) = 42[/tex]
[tex]4.(x - 3)(x + 3) = 40[/tex]
[tex]5.9x {}^{2} - 4 = 0[/tex]
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Sagot :

Piyanistaviz

Item 1

[tex] {x}^{2} = 2x \\ {x}^{2} - 2x = 0 \\ x(x - 2) = 0 [/tex]

Meaning, x = 0 and x = 2.

Item 2

[tex]x(x + 1) = 12 \\ {x}^{2} + x - 12 = 0 \\ (x + 4)(x - 3) = 0 [/tex]

Meaning, x = -4 and x = 3.

Item 3

[tex]x(x + 1) = 42 \\ {x}^{2} + x - 42 = 0 \\ (x + 7)(x - 6) = 0[/tex]

Meaning, x = -7 and x = 6.

Item 4

[tex](x - 3)(x + 3) = 40 \\ {x}^{2} - 9 = 40 \\ {x}^{2} - 49 = 0 \\ (x + 7)(x - 7) = 0[/tex]

Meaning, x = ±7.

Item 5

[tex]9 {x}^{2} - 4 = 0 \\ (3x + 2)(3x - 2) = 0[/tex]

Meaning, x = ± 2/3.

Hope this helps.

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