Question

Solve the quadratic equation by completing the square. X^2+14x+38=0

Can you explain the steps too so I can understand it better. Also if there are more than one solution can you add all of the solutions. Thank you!

Answer 1

`\rm x = - 7 \pm √(11)`

Explanation:

Solve for x over the real numbers:

`\longrightarrow` x² + 14x + 38 = 0

Subtract 38 from both sides:

`\longrightarrow` x² + 14x + 38 - 38 = 0 - 38

`\longrightarrow` x² + 14x = -38

Add 49 to both sides:

`\longrightarrow` x² + 14x + 49 = 49 - 38

`\longrightarrow` x² + 14x + 49 = 11

Write the left hand side as a square:

`\longrightarrow` x² + 7x + 7x + 49 = 11

`\longrightarrow` x(x + 7) + 7(x + 7) = 11

`\longrightarrow` (x + 7)(x + 7) = 11

`\longrightarrow` (x + 7)² = 11

Take the square root of both sides:

`\longrightarrow`
`\sf \sqrt{{(x + 7)}^(2)} = \pm √(11)`

`\longrightarrow`
`\sf x + 7 = \pm √(11)`

Subtract 7 from both sides:

`\longrightarrow`
`\sf x = - 7 \pm √(11)`