Solve by completing the square x2-7x+10=0
Well, let's start by completing the square! It's like completing a puzzle, but with numbers instead. So, for the equation x^2 - 7x + 10 = 0, we want to get that x by itself!
First, let's take care of the constant term, which is 10. We need to divide it by 2, and then square the result. So we have (10 / 2)^2 = 5^2 = 25.
Now, we add this magical number 25 to both sides of the equation. So we have x^2 - 7x + 10 + 25 = 25.
Now, let's simplify the equation. We can combine the 10 and 25 to get x^2 - 7x + 35 = 25.
Almost there! Now, since we completed the square, we can write the left side as a perfect square trinomial. So it becomes (x - 3.5)^2 = 25.
Taking the square root of both sides, we get x - 3.5 = ±5.
Now, let's solve for x. Adding 3.5 to both sides, we have x = 3.5 ± 5.
So the solutions to the equation x^2 - 7x + 10 = 0 are x = 3.5 + 5 and x = 3.5 - 5.
And there you have it! The clowntastic solution to completing the square.
To solve the quadratic equation x^2 - 7x + 10 = 0 by completing the square, follow these steps:
Step 1: Move the constant term to the right side of the equation:
x^2 - 7x = -10
Step 2: Take half of the coefficient of the x-term and square it. Add this value to both sides of the equation:
x^2 - 7x + (-7/2)^2 = -10 + (-7/2)^2
Simplifying this equation gives:
x^2 - 7x + 49/4 = -10 + 49/4
Step 3: Combine the constants on the right side:
x^2 - 7x + 49/4 = -40/4 + 49/4
This gives us:
x^2 - 7x + 49/4 = 9/4
Step 4: Rewrite the left side of the equation as a perfect square:
(x - 7/2)^2 = 9/4
Step 5: Take the square root of both sides:
√(x - 7/2)^2 = ±√(9/4)
Simplifying this equation, we have:
x - 7/2 = ±3/2
Step 6: Solve for x by adding 7/2 to both sides:
x = 7/2 ± 3/2
This gives us two solutions:
x = (7 + 3)/2 = 10/2 = 5
x = (7 - 3)/2 = 4/2 = 2
Therefore, the solutions to the quadratic equation x^2 - 7x + 10 = 0 are x = 5 and x = 2.
To solve the quadratic equation x^2 - 7x + 10 = 0 by completing the square, you can follow these steps:
Step 1: Move the constant term to the right side of the equation:
x^2 - 7x = -10
Step 2: Take half of the coefficient of x (-7/2) and square it to get (7/2)^2 = 49/4:
x^2 - 7x + 49/4 = -10 + 49/4
Step 3: Simplify the right side of the equation:
x^2 - 7x + 49/4 = -40/4 + 49/4
x^2 - 7x + 49/4 = 9/4
Step 4: Rewrite the left side of the equation as a perfect square:
(x - 7/2)^2 = 9/4
Step 5: Take the square root of both sides:
√[(x - 7/2)^2] = ±√(9/4)
Step 6: Solve for x by considering both positive and negative square roots separately:
x - 7/2 = ±3/2
Step 7: Add 7/2 to both sides of the equation to isolate x:
x = 7/2 ± 3/2
Step 8: Simplify the expression:
x = (7 ± 3)/2
So the solutions to the quadratic equation x^2 - 7x + 10 = 0 are x = (7 + 3)/2 = 5 and x = (7 - 3)/2 = 2.
x^2 - 7x + 10 = 0
x^2 - 7x = -10
x^2 - 7x + (7/2)^2 = -10 + (7/2)^2
(x - 7/2)^2 = (-40+49)/4 = 9/4
x - 7/2 = ±3/2
x = (7±3)/2
x = 2 or 5
check: x^2-7x+10 = (x-2)(x-5)