completing the square of x^2-3x-8=0
x^2-3x-8=0
x^2 - 3x = 8
x^2 - 3x + 9/4 = 8 + 9/4
(x - 3/2)^2 = 41/4
x - 3/2 = ±√41/2
x = 3/2 ± √41/2 = (3 ±√41)/2
to find the term to be added to each side,
take 1/2 the coefficient of the x term , then square it
that is,
1/2 of 3 is 3/2, square it to get 9/4
To complete the square for the quadratic equation x^2 - 3x - 8 = 0, follow these steps:
Step 1: Move the constant term to the other side of the equation:
x^2 - 3x = 8
Step 2: Take half of the coefficient of x and square it. Add this value to both sides of the equation:
x^2 - 3x + (3/2)^2 = 8 + (3/2)^2
x^2 - 3x + 9/4 = 8 + 9/4
Step 3: Simplify the right side of the equation:
x^2 - 3x + 9/4 = 32/4 + 9/4
x^2 - 3x + 9/4 = 41/4
Step 4: Rewrite the left side of the equation as a perfect square trinomial:
(x - 3/2)^2 = 41/4
Step 5: Take the square root of both sides:
x - 3/2 = ±√(41/4)
Step 6: Solve for x by adding 3/2 to both sides:
x = 3/2 ± √(41/4)
So the solutions for the quadratic equation x^2 - 3x - 8 = 0 after completing the square are:
x = 3/2 + √(41/4)
x = 3/2 - √(41/4)
To complete the square for the quadratic equation \(x^2-3x-8=0\), follow these steps:
1. Move the constant term (-8) to the other side of the equation, so it becomes:
\(x^2 - 3x = 8\)
2. Take half of the coefficient of the \(x\) term (-3 in this case), square it, and add it to both sides of the equation. This step ensures that the left side of the equation can be factored into a perfect square trinomial. Half of -3 is -1.5, and squared it becomes 2.25. So, the equation becomes:
\(x^2 - 3x + 2.25 = 8 + 2.25\)
3. Simplify the equation:
\(x^2 - 3x + 2.25 = 10.25\)
4. Factor the left side of the equation so that it can be written as a perfect square trinomial:
\((x - 1.5)^2 = 10.25\)
Now, the equation is in a completed square form.
To solve for \(x\), take the square root of both sides:
\(\sqrt{(x - 1.5)^2} = \sqrt{10.25}\)
\(x - 1.5 = \pm \sqrt{10.25}\)
5. Solve for \(x\) by adding 1.5 to both sides of the equation:
\(x = 1.5 \pm \sqrt{10.25}\)
So, the solutions for the quadratic equation \(x^2-3x-8=0\) after completing the square are \(x = 1.5 + \sqrt{10.25}\) and \(x = 1.5 - \sqrt{10.25}\).