Solve each of the following quadratic equations by completing the aquare.
1. x^2-6x-3=0
2. 2x^2+10x+11=0
Step 1.
Move the constant to the other side.
X^2 -6x + ?? = 3 + ??
To find ??, take 1/2 the x term and square it, then add it to both sides; therefore, 1/2*6 = 3 and 3^2 = 9.
X^2 -6x + 9 = 3 + 9
X^2 -6x + 9 = 12.
(X+3)^2 = 12
X+3 = sq rt 12
Solve for X. Post your work if you get stuck. The other one is worked the same way.
To solve the quadratic equation x^2 - 6x - 3 = 0 by completing the square, follow these steps:
Step 1: Move the constant to the other side.
x^2 - 6x - 3 + 3 = 0 + 3
x^2 - 6x = 3
Step 2: Complete the square. To do this, take half of the coefficient of x (-6/2 = -3) and square it (-3^2 = 9). Add this value to both sides of the equation.
x^2 - 6x + 9 = 3 + 9
x^2 - 6x + 9 = 12
Step 3: Rewrite the left side as a perfect square.
(x - 3)^2 = 12
Step 4: Solve for x by taking the square root of both sides.
x - 3 = ±√12
Step 5: Simplify the square root of 12.
x - 3 = ±2√3
Step 6: Solve for x by adding 3 to both sides.
x = 3 ± 2√3
Therefore, the solutions to the quadratic equation x^2 - 6x - 3 = 0 are x = 3 + 2√3 and x = 3 - 2√3.
You can follow the same steps to solve the second quadratic equation, 2x^2 + 10x + 11 = 0.