How do I solve a quadratic equation x^2 - x = 30 by completing the square-
I don't understand-could someone just explain the steps to solving this
Thank you
I found this example on purplemath
You coul use this and apply knowledge.
This is the original equation. x2 + 6x – 7 = 0
Move the loose number over to the other side. x2 + 6x = 7
Take half of the x-term (that is, divide it by two) (and don't forget the sign!), and square it. Add this square to both sides of the equation.
Convert the left-hand side to squared form. Simplify the right-hand side. (x + 3)2 = 16
Square-root both sides. Remember to do "±" on the right-hand side. x + 3 = ± 4
Solve for "x =". Remember that the "±" gives you two solutions. Simplify as necessary. x = – 3 ± 4
= – 3 – 4, –3 + 4
= –7, +1
you're welcome!
We should hook up
Ok what’s your digits
Certainly! I can explain the steps to solving a quadratic equation using the method of completing the square.
Step 1: Start with the given quadratic equation: x^2 - x = 30.
Step 2: Move the constant term (30) to the right side of the equation by subtracting it from both sides: x^2 - x - 30 = 0.
Step 3: Look at the coefficient of the x-term, which is -1 in this case. Divide it by 2 and square the result: (-1/2)^2 = 1/4.
Step 4: Add the result obtained in Step 3 to both sides of the equation: x^2 - x + 1/4 = 30 + 1/4.
Step 5: Simplify both sides of the equation if necessary: (x - 1/2)^2 = 30 + 7/4.
Step 6: Combine the terms on the right side of the equation: (x - 1/2)^2 = 123/4.
Step 7: Take the square root of both sides of the equation to isolate x - 1/2: x - 1/2 = ±√(123/4).
Step 8: Simplify the square root on the right side if possible.
Step 9: Solve for x by adding 1/2 to both sides of the equation: x = 1/2 ±√(123/4).
So the solutions to the quadratic equation x^2 - x = 30 are x = 1/2 + √(123/4) and x = 1/2 - √(123/4).