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Math  /  Algebra

QuestionEg4. Solving by completing the square Solve by completing the square: x2+8x+3=0x^{2}+8 x+3=0

Studdy Solution

STEP 1

1. The equation x2+8x+3=0 x^2 + 8x + 3 = 0 is a quadratic equation.
2. We will solve this equation by completing the square.
3. Completing the square involves creating a perfect square trinomial from the quadratic expression.

STEP 2

1. Move the constant term to the other side of the equation.
2. Complete the square for the quadratic expression.
3. Solve for x x by taking the square root of both sides.
4. Simplify to find the solutions.

STEP 3

Start with the given equation and move the constant term to the right side:
x2+8x+3=0 x^2 + 8x + 3 = 0
Subtract 3 from both sides:
x2+8x=−3 x^2 + 8x = -3

STEP 4

To complete the square, take half of the coefficient of x x , square it, and add it to both sides. The coefficient of x x is 8, so half of it is 4, and squaring it gives 16:
Add 16 to both sides:
x2+8x+16=−3+16 x^2 + 8x + 16 = -3 + 16
x2+8x+16=13 x^2 + 8x + 16 = 13

STEP 5

Now, the left side is a perfect square trinomial. Rewrite it as a square of a binomial:
(x+4)2=13 (x + 4)^2 = 13
Take the square root of both sides:
x+4=±13 x + 4 = \pm \sqrt{13}

STEP 6

Solve for x x by isolating it on one side:
x=−4±13 x = -4 \pm \sqrt{13}
This gives us two solutions:
x=−4+13andx=−4−13 x = -4 + \sqrt{13} \quad \text{and} \quad x = -4 - \sqrt{13}
The solutions to the equation are:
x=−4+13andx=−4−13 x = -4 + \sqrt{13} \quad \text{and} \quad x = -4 - \sqrt{13}

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