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aleksklad [387]
3 years ago
5

Solve by completing the square: 8x^2+16x=42 Please show steps

Mathematics
1 answer:
lakkis [162]3 years ago
7 0
Hi,

Equation:

8 {x}^{2} + 16x = 42

Work:

Divide both sides of equation with 2.

4 {x}^{2} + 8x = 21

Move constant 21 to the left and change its sign.

4 {x}^{2} + 8x - 21 = 0

Write 8x as a difference.

4 {x}^{2} + 14x - 6x - 21 = 0

Factor out 2x from the expression.

2x \times (2x + 7) - 6x - 21 = 0

Factor out 2x + 7 from the expression.

2x \times (2x + 7) - 3(2x + 7) = 0 \\ (2x + 7) \times (2x - 3) = 0

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

2x + 7 = 0 \\ 2x - 3 = 0

Solve equation for x.

x = - \frac{7}{2} \\ 2x -3 = 0 \\ x = \frac{3}{2}

The final solutions are:

x = - \frac{7}{2} \: and \: y = \frac{3}{2}

Hope this helps.
r3t40
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