Solve the equation by completing the square x^2 -18 x =19
a. 1; 19
b. -1;19***
c. 3;6
d. 3:1
correct
To solve the equation x^2 - 18x = 19 by completing the square, follow these steps:
Step 1: Move the constant term to the right side of the equation:
x^2 - 18x - 19 = 0
Step 2: Take half of the coefficient of x (which is -18), square it, and add it to both sides of the equation:
x^2 - 18x + (-9)^2 - 9^2 - 19 = (-9)^2
x^2 - 18x + 81 - 162 - 19 = 81
x^2 - 18x - 100 = 0
Step 3: Factor or use the quadratic formula to solve the equation:
(x - 10)(x + 10) = 0
Step 4: Set each factor equal to zero and solve for x:
x - 10 = 0 or x + 10 = 0
For x - 10 = 0, adding 10 to both sides gives:
x = 10
For x + 10 = 0, subtracting 10 from both sides gives:
x = -10
Therefore, the solutions to the equation x^2 - 18x = 19 are x = 10 and x = -10.
To solve the quadratic equation x^2 - 18x = 19 by completing the square, follow these steps:
Step 1: Move the constant term to the other side of the equation.
x^2 - 18x - 19 = 0
Step 2: Take half of the coefficient of the x-term, square it, and add it to both sides of the equation.
Coefficient of x-term = -18
(-18/2)^2 = 81
x^2 - 18x + 81 - 19 = 81
Simplified equation: x^2 - 18x + 62 = 0
Step 3: Factor the trinomial on the left side of the equation, if possible. If factoring is not possible, move to the next step.
(x - 9)^2 - 17 = 0
Step 4: Set the equation equal to zero.
(x - 9)^2 - 17 = 0
Step 5: Add 17 to both sides of the equation.
(x - 9)^2 = 17
Step 6: Take the square root of both sides of the equation, considering both the positive and negative square roots.
x - 9 = ± √17
Step 7: Solve for x by adding 9 to both sides of the equation.
x = 9 ± √17
The solutions to the given equation are:
a. 1; 19
b. -1; 19
c. 3; 6
d. 3:1
Among the given options, the correct solution is b. -1; 19.