Question

решите уравнение с помощью выделения полного квадрата
${x}^{2} - 6x + 8 = 0$
${x}^{2} + 3x - 40 = 0$
${5x}^{2} + 3x - 2 = 0$
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Answer 1

Номер 1

${x}^{2} - 6x + 8 = 0 \\ {x}^{2} - 2x - 4x + 8 = 0 \\ x(x - 2) - 4(x - 2) = 0 \\ (x - 2)(x - 4) = 0 \\ x _{1} = 2 \\ x _{2} = 4$

Номер 2

${x}^{2} + 3x - 40 = 0 \\ {x}^{2} + 8x - 5x - 40 = 0 \\ x(x +8 ) - 5(x + 8) = 0 \\ (x + 8)(x - 5) = 0 \\ x _{1} = - 8 \\ x _{2} = 5$

Номер 3

${5x}^{2} + 3x - 2 = 0 \\ {5x}^{2} + 5x - 2x- 2 = 0 \\ 5x(x +1 ) - 2(x + 1) \\ (5x - 2)(x + 1) = 0 \\ x _{1} = - 1 \\ x _{2} = \frac{2}{5}=0.4$