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
