2x^2-5x-12=0
solve by completing the square.
please explain how it's sovled.
2x^2-5x-12 = 0
2(x^2 - 5/2) = 12
x^2 - 5/2 = 6
x^2 - 5/2 + (5/4)^2 = 6 + (5/4)^2
(x - 5/4)^2 = 6 + 25/16 = 121/16
x - 5/4 = ±11/4
x = 5/4 ± 11/4
x = 4 or -3/2
In google type :
quadratic equation online
When you see list of results click on :
Free Online Quadratic Equation Solver: Solve by Quadratic Formula
When page be open click on :
Solve by Completing the Square
then type :
2x^2-5x-12=0
and click option :
solve it!
You will see solution step by step
this is so helpful
. 2x² + 5x = 12 *
To solve the quadratic equation 2x^2 - 5x - 12 = 0 by completing the square, follow these steps:
Step 1: Ensure that the coefficient of x^2 is 1 by dividing both sides of the equation by the coefficient of x^2. In this case, divide the equation by 2 to get:
x^2 - (5/2)x - 6 = 0
Step 2: Move the constant term to the other side of the equation. In this case, add 6 to both sides:
x^2 - (5/2)x = 6
Step 3: Take the coefficient of x (in this case, -5/2) and divide it by 2. Square that value and add it to both sides of the equation. The left side will form a perfect square trinomial.
To calculate the square of -5/2 divided by 2, we get:
(-5/2)^2 = 25/4
Adding this to both sides of the equation gives:
x^2 - (5/2)x + 25/4 = 6 + 25/4
Simplifying the right side:
x^2 - (5/2)x + 25/4 = 24/4 + 25/4
Combining like terms:
x^2 - (5/2)x + 25/4 = 49/4
Step 4: Rewrite the left side of the equation as a perfect square binomial. Take the square root of the constant term on the right side of the equation and add or subtract it to the equation.
The square root of 49/4 is 7/2. So the equation becomes:
(x - 5/2)^2 = 49/4
Step 5: Take the square root of both sides of the equation:
√((x - 5/2)^2) = ±√(49/4)
Simplifying:
x - 5/2 = ±7/2
Step 6: To solve for x, isolate x on the left side by adding 5/2 to both sides:
x = 5/2 ± 7/2
Simplifying:
x = (5 ± 7)/2
Therefore, the solutions to the quadratic equation 2x^2 - 5x - 12 = 0, when solved by completing the square, are:
x = (5 + 7)/2 = 12/2 = 6
x = (5 - 7)/2 = -2/2 = -1
Hence, the solutions are x = 6 and x = -1.