What number is added to both sides of the equation x2 8x 3 0 to solve it by completing the square?

This calculator is a quadratic equation solver that will solve a second-order polynomial equation in the form ax2 + bx + c = 0 for x, where a ≠ 0, using the completing the square method.

The calculator solution will show work to solve a quadratic equation by completing the square to solve the entered equation for real and complex roots.

Completing the square when a is not 1

To complete the square when a is greater than 1 or less than 1 but not equal to 0, factor out the value of a from all other terms.

For example, find the solution by completing the square for:

\( a \ne 1, a = 2 \) so divide through by 2

\( \dfrac{2}{2}x^2 - \dfrac{12}{2}x + \dfrac{7}{2} = \dfrac{0}{2} \)

which gives us

\( x^2 - 6x + \dfrac{7}{2} = 0 \)

Now, continue to solve this quadratic equation by completing the square method.

Completing the square when b = 0

When you do not have an x term because b is 0, you will have a easier equation to solve and only need to solve for the squared term.

For example: Solution by completing the square for:

Eliminate b term with 0 to get:

Keep \( x \) terms on the left and move the constant to the right side by adding it on both sides

Take the square root of both sides

therefore

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Solve by completing the square. $$ x 2+8 x+3=0 $$

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Using the completing the square method:

1. Notice (x+4)2 = x2 + 8x +16 which differs from the question by a constant

2. So we can write: 

x2 + 8x + 3 = (x+4)2 - 13      (check this yourself if you don't see it immediately)

3. So from the question we get:

(x+4)2 -13 = 0

(x+4)2 = 13     (by adding 13)

x+4 = +-sqrt(13)    (square root remembering to include the +-)

x = -4 +-sqrt(13)      (subtracting 4)

So we have answers of:

x = - 4 + sqrt(13)

x = - 4 - sqrt(13)

which can both be checked by substitution into the original equation.