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

Answer:

$\rm x = - 7 \pm \sqrt{11}$

Step-by-step 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:

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

$\longrightarrow$ $\sf x + 7 = \pm \sqrt{11}$

Subtract 7 from both sides:

$\longrightarrow$ $\sf x = - 7 \pm \sqrt{11}$