2x^2-6x-36=0 Solve by completing the square
divide by 2 and bring constant to the right side
x^2 - 3x + .... = 18
x^2 - 3x + 9/4 = 18 + 9/4
(x - 3/2)^2 = 81/4
x - 3/2 = ± 9/2
x = 3/2 ± 9/2
x = -3 or x = 6
Understood 👍🏻
To solve the quadratic equation 2x^2 - 6x - 36 = 0 by completing the square, follow these steps:
Step 1: Divide the entire equation by the coefficient of x^2 to make the coefficient of x^2 equal to 1:
(2x^2 - 6x - 36) / 2 = 0 / 2
x^2 - 3x - 18 = 0
Step 2: Move the constant term (in this case, -18) to the other side of the equation:
x^2 - 3x = 18
Step 3: Take half of the coefficient of x (-3) and square it. Then add that value to both sides of the equation. This completes the square on the left side of the equation:
x^2 - 3x + (3/2)^2 = 18 + (3/2)^2
x^2 - 3x + 9/4 = 18 + 9/4
Step 4: Simplify the right side of the equation:
x^2 - 3x + 9/4 = 72/4 + 9/4
x^2 - 3x + 9/4 = 81/4
Step 5: Factor the trinomial on the left side of the equation:
(x - 3/2)^2 = 81/4
Step 6: Take the square root of both sides of the equation:
√[(x - 3/2)^2] = ±√(81/4)
Step 7: Simplify:
x - 3/2 = ±(9/2)
Step 8: Solve for x:
For x - 3/2 = 9/2:
x = 3/2 + 9/2 = 12/2 = 6
For x - 3/2 = -9/2:
x = 3/2 - 9/2 = -6/2 = -3
Therefore, the solutions to the equation 2x^2 - 6x - 36 = 0 are x = 6 and x = -3.
To solve the quadratic equation 2x^2 - 6x - 36 = 0 by completing the square, follow these steps:
Step 1: Divide the equation by the coefficient of x^2 to make the coefficient equal to 1:
x^2 - 3x - 18 = 0
Step 2: Move the constant term to the other side of the equation:
x^2 - 3x = 18
Step 3: Take half of the coefficient of x (which is -3) and square it:
(-3/2)^2 = 9/4
Step 4: Add the result from step 3 to both sides of the equation:
x^2 - 3x + 9/4 = 18 + 9/4
Step 5: Simplify both sides of the equation:
(x - 3/2)^2 = (72/4) + (9/4)
(x - 3/2)^2 = 81/4
Step 6: Take the square root of both sides of the equation:
x - 3/2 = ± √(81/4)
x - 3/2 = ± (9/2)
Step 7: Add 3/2 to both sides of the equation:
x = 3/2 ± 9/2
Step 8: Simplify the results:
x1 = (3 + 9)/2 = 12/2 = 6
x2 = (3 - 9)/2 = -6/2 = -3
Therefore, the solutions to the quadratic equation 2x^2 - 6x - 36 = 0 are x = 6 and x = -3.