Solve the quadratic equation by completing the square.
x^2-2x-6=0
To solve for x by the method of completing the square, follow the steps below:
Step 1: Rearrange the equation to set it to zero.
x^2 - 2x - 6 = 0
Step 2: Transfer the c (the constant term) to the right side of the equation.
x^2 - 2x = 6
Step 3: Add the square of half the coefficient of x to both sides to complete the square. Half the coefficient of x is -2/2 = -1. The square of -1 is 1.
x^2 - 2x + 1 = 6 + 1
(x - 1)^2 = 7
Step 4: Take the square root of both sides to solve for x.
x - 1 = ±sqrt(7)
Step 5: Add 1 to both sides to isolate x.
x = 1 ± sqrt(7)
Therefore, the solutions to the equation x^2 - 2x - 6 = 0 by completing the square are x = 1 + sqrt(7) and x = 1 - sqrt(7).
To solve the quadratic equation x^2-2x-6=0 by completing the square, follow these steps:
Step 1: Move the constant term to the right side:
x^2 - 2x = 6
Step 2: Take half of the coefficient of the x-term (-2), square it, and add it to both sides of the equation:
x^2 - 2x + (-2/2)^2 = 6 + (-2/2)^2
x^2 - 2x + 1 = 6 + 1
Step 3: Simplify the equation:
x^2 - 2x + 1 = 7
Step 4: Rewrite the left side of the equation as a perfect square trinomial:
(x - 1)^2 = 7
Step 5: Take square roots on both sides of the equation and solve for x:
x - 1 = ±√7
Step 6: Add 1 to both sides to isolate x:
x = 1 ±√7
Therefore, the solutions to the quadratic equation x^2 - 2x - 6 = 0 are x = 1 + √7 and x = 1 - √7.
To solve the quadratic equation by completing the square, follow these steps:
Step 1: Make sure the equation is in the form of "ax^2 + bx + c = 0".
Given equation: x^2 - 2x - 6 = 0
Step 2: Move the constant term (c) to the other side of the equation.
x^2 - 2x = 6
Step 3: Divide the coefficient of x by 2, square the result, and add it to both sides of the equation.
Coefficient of x: -2
(-2/2)^2 = (-1)^2 = 1
x^2 - 2x + 1 = 6 + 1
x^2 - 2x + 1 = 7
Step 4: Rewrite the left side of the equation as a perfect square trinomial.
(x - 1)^2 = 7
Step 5: Take the square root of both sides of the equation and solve for x.
√((x - 1)^2) = ±√7
x - 1 = ±√7
Step 6: Solve for x by adding 1 to both sides of the equation.
x = 1 ± √7
Therefore, the solutions to the quadratic equation x^2 - 2x - 6 = 0, when completed by the square, are x = 1 + √7 and x = 1 - √7.