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11 - 1. Solve the quadratic equation by completing the square x² + 4x = 5 2. Solve the quadratic equation by factoring x2 + 6x + 9​

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UK2019idn

✏️QUADRATIC

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1. Solve the quadratic equation by completing the square x² + 4x = 5

  • [tex] \sf {x}^{2} + 4x - 5 = 0[/tex]

  • [tex] \sf {x}^{2} + 4x = 5[/tex]

  • [tex] \begin{gathered} \sf \bigg[ 4 \times \frac{1}{2} \bigg]^{2} = 4 \end{gathered}[/tex]

  • [tex] \sf {x}^{2} + 4x + 4 = 5 + 4[/tex]

  • [tex] \sf(x + 2)^{2} = 9[/tex]

  • [tex] \sf \sqrt{(x + 2)^{2} } = \: ± \: \sqrt{9} [/tex]

  • [tex] \sf x + 2 = \: ± \: 3[/tex]

  • [tex] \sf x = - 2 \: ± \: 3[/tex]

Solution 1:

  • [tex] \sf x = - 2 + 3[/tex]

  • [tex] \sf x = 1[/tex]

Solution 2:

  • [tex] \sf x = - 2 - 3[/tex]

  • [tex] \sf x = -5[/tex]

[tex] \large \therefore\boxed{ \sf{ \green{x = 1,x = - 5}}}[/tex]

[tex] \large \sf [/tex]

2. Solve the quadratic equation by factoring x² + 6x + 9 = 0

  • [tex] \sf {x}^{2} + 6x + 9 = 0[/tex]

  • [tex] \sf (x + 3)(x + 3) = 0[/tex]

  • [tex] \sf x + 3 = 0 \: \: \: \: ; \: \: \: \: x + 3 = 0[/tex]

  • [tex] \sf x = - 3 \: \: \: \: ; \: \: \: \: x = - 3[/tex]

[tex] \large \therefore\boxed{ \sf{ \green{x = - 3,x = - 3}}}[/tex]

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