Solve the quadratic equation by completing the square.
x^2-14x-2=0
First, we start by moving the constant term to the right side of the equation:
x² - 14x = 2
Then, we need to complete the square on the left-hand side. This means taking half of the coefficient of x, squaring it, and adding it to both sides of the equation.
Half of -14 is -7, and (-7)² = 49.
So, we add 49 to both sides:
x² - 14x + 49 = 2 + 49
(x - 7)² = 51
Next, we take the square root of both sides. Remembering to consider both the positive and negative square roots:
x - 7 = ± √51
x = 7 ± √51
So, the solutions to the equation are x = 7 + sqrt(51) , 7 - sqrt(51).
Step 1: Move the constant term to the other side of the equation:
x^2 - 14x = 2
Step 2: Take half of the coefficient of the x term (-14) and square it:
(-14/2)^2 = (-7)^2 = 49
Step 3: Add the squared value obtained in step 2 to both sides of the equation:
x^2 - 14x + 49 = 2 + 49
x^2 - 14x + 49 = 51
Step 4: Rewrite the left side of the equation as a perfect square trinomial:
(x - 7)^2 = 51
Step 5: Take the square root of both sides of the equation:
√(x - 7)^2 = ±√51
x - 7 = ±√51
Step 6: Solve for x:
x = 7 ±√51
So, the solutions to the given quadratic equation are x = 7 + √51 and x = 7 - √51.
To solve the quadratic equation x^2-14x-2=0 by completing the square, follow these steps:
Step 1: Move the constant term to the right side:
x^2 - 14x = 2
Step 2: Take half of the coefficient of x (in this case, -14) and square it:
(14/2)^2 = 7^2 = 49
Step 3: Add the value obtained in step 2 to both sides of the equation:
x^2 - 14x + 49 = 2 + 49
x^2 - 14x + 49 = 51
Step 4: Rewrite the left side of the equation as a perfect square:
(x - 7)^2 = 51
Step 5: Take the square root of both sides of the equation to isolate x:
√((x - 7)^2) = ±√51
x - 7 = ±√51
Step 6: Add 7 to both sides of the equation:
x = 7 ±√51
Therefore, the solutions to the quadratic equation x^2-14x-2=0 are x = 7 + √51 and x = 7 - √51.