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r3t40
Hi,

Equation:

[tex]8 {x}^{2} + 16x = 42[/tex]

Work:

Divide both sides of equation with 2.

[tex]4 {x}^{2} + 8x = 21[/tex]

Move constant 21 to the left and change its sign.

[tex]4 {x}^{2} + 8x - 21 = 0[/tex]

Write 8x as a difference.

[tex]4 {x}^{2} + 14x - 6x - 21 = 0[/tex]

Factor out 2x from the expression.

[tex]2x \times (2x + 7) - 6x - 21 = 0[/tex]

Factor out 2x + 7 from the expression.

[tex]2x \times (2x + 7) - 3(2x + 7) = 0 \\ (2x + 7) \times (2x - 3) = 0[/tex]

When the product of factors is 0, at least one factor is 0.

[tex]2x + 7 = 0 \\ 2x - 3 = 0[/tex]

Solve equation for x.

[tex]x = - \frac{7}{2} \\ 2x -3 = 0 \\ x = \frac{3}{2} [/tex]

The final solutions are:

[tex]x = - \frac{7}{2} \: and \: y = \frac{3}{2} [/tex]

Hope this helps.
r3t40

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