Root x +x square=y
To solve the equation √(x) + x^2 = y, we need to isolate the variable x.
Step 1: Start by subtracting y from both sides of the equation:
√(x) + x^2 - y = 0
Step 2: Now, let's focus on eliminating the square root term. To do this, we need to isolate the square root term on one side of the equation. Rearrange the equation as follows:
√(x) = y - x^2
Step 3: To remove the square root, we square both sides of the equation:
(√(x))^2 = (y - x^2)^2
Simplifying the equation gives us:
x = (y - x^2)^2
Step 4: Expand the equation on the right-hand side:
x = (y - x^2)(y - x^2)
Step 5: Distribute the terms on the right-hand side:
x = y^2 - 2xy^2 + x^4
Step 6: Rearrange the terms to have the equation in quadratic form:
x^4 - 2xy^2 + x - y^2 = 0
At this stage, we have transformed the equation into a quartic equation. If there is a specific value of y given, you can substitute it into the equation and solve for x either graphically or using numerical methods.