What's the answer to
1^2-(2-x)^2=2^2-x^2
The answer said x =7/4
But no matter how I tried. I couldn't get that
1^2-(2-x)^2=2^2-x^2
1 - (4 - 4x + x^2) = 4 - x^2
1 - 4 + 4x - x^2 = 4 - x^2
4x = 7
x = 7/4
I don't understand why a textbook would write a term
as 1^2 and 2^2 in an equation.
That is just silly.
Thank you. I forgot the brackets
To solve the equation 1^2 - (2-x)^2 = 2^2 - x^2, we can methodically simplify the equation and then solve for x.
Let's break down the steps to solve the equation:
Step 1: Simplify both sides of the equation.
By expanding the terms inside the parentheses and simplifying, we get:
1 - (4 - 4x + x^2) = 4 - x^2
Step 2: Continue simplifying.
Distribute the negative sign into the parentheses on the left side:
1 - 4 + 4x - x^2 = 4 - x^2
Combine like terms on both sides of the equation:
4x - x^2 - 3 = 0
Step 3: Rearrange the equation to explicitly show x as a quadratic equation:
Rearranging the expression, we get:
-x^2 + 4x - 3 = 0
Step 4: Solve the quadratic equation.
To solve the quadratic equation, we can use the quadratic formula:
x = (-b±√(b^2-4ac)) / 2a
For our quadratic equation -x^2 + 4x - 3 = 0, the values for a, b, and c are:
a = -1, b = 4, c = -3
Substituting these values into the quadratic formula, we get:
x = (-(4)±√((4)^2-4(-1)(-3))) / 2(-1)
Simplifying further:
x = (-4±√(16-12)) / -2
x = (-4±√(4)) / -2
x = (-4±2) / -2
x = (2-4) / -2 or x = (-2-4) / -2
Simplifying the expressions inside the brackets, we have:
x = -2/-2 or x = -6/-2
x = 1 or x = 3
Therefore, the solutions to the equation could be x = 1 or x = 3.
Since the given answer is x = 7/4, it appears that there might have been an error in the original problem or solution provided. Double-checking the equation and the calculations is always advisable to ensure accurate results.