x^2-6x-7=0 Completing the square
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To complete the square for the quadratic equation x^2 - 6x - 7 = 0, follow these steps:
Step 1: Move the constant term to the right side of the equation:
x^2 - 6x = 7
Step 2: Divide the coefficient of x by 2 and square it. Add this value to both sides of the equation:
x^2 - 6x + 9 = 7 + 9
(x - 3)^2 = 16
Step 3: Take the square root of both sides to solve for x:
√((x - 3)^2) = √16
(x - 3) = ±√16
Step 4: Simplify the square root:
(x - 3) = ±4
Step 5: Solve for x by adding 3 to both sides:
x = 3 ± 4
So, the solutions to the equation x^2 - 6x - 7 = 0 after completing the square are:
x = 3 + 4
x = 3 - 4
Simplifying, we get:
x = 7 or x = -1
Sure, I can help you with completing the square to solve the quadratic equation.
To complete the square for the given equation, follow these steps:
Step 1: Move the constant term to the right side of the equation:
x^2 - 6x = 7
Step 2: Take the coefficient of x (in this case, -6) and divide it by 2. Then square the result. Add this squared value to both sides of the equation:
x^2 - 6x + (-6/2)^2 = 7 + (-6/2)^2
x^2 - 6x + 9 = 7 + 9
x^2 - 6x + 9 = 16
Step 3: Rewrite the left side of the equation in the form of a perfect square trinomial:
(x - 3)^2 = 16
Step 4: Take the square root of both sides of the equation, considering both the positive and negative square roots:
x - 3 = ±√16
Step 5: Simplify both sides of the equation:
x - 3 = ±4
Step 6: Solve for x by adding 3 to both sides of the equation:
x = 3 ± 4
So the solutions to the quadratic equation are x = 7 and x = -1.
what is half of -6 squared: 6/2=3, squared , 9
x^2-6x+9 -7=9
(x-3)^2 =16
take the square root of each side.
x-3= +-4
x=7, or -1