Example Question - isolate square roots
Here are examples of questions we've helped users solve.
Solving an Equation with Square Roots
The equation provided in the image is: √(x+2) + √(x−2) = 5/2 To solve this equation for x, follow these steps: 1. Isolate one of the square roots on one side of the equation. Let's move √(x−2) to the right side: √(x+2) = 5/2 − √(x−2) 2. Now, square both sides to eliminate the square root: (√(x+2))^2 = (5/2 − √(x−2))^2 x + 2 = (5/2)^2 − 2*(5/2)*√(x−2) + (√(x−2))^2 x + 2 = 25/4 − 5√(x−2) + x − 2 3. Simplify and isolate the term involving the square root: 25/4 − 4 = 5√(x−2) 25 − 16 = 20√(x−2) 9 = 20√(x−2) 4. Divide both sides by 20 to isolate the square root: 9/20 = √(x−2) 5. Now, square both sides again to eliminate the square root: (9/20)^2 = (x−2) 81/400 = x−2 6. Add 2 to both sides to solve for x: x = 81/400 + 2 x = 81/400 + 800/400 x = 881/400 Therefore, the solution to the original equation is x = 881/400.
Solving a Square Root Equation
The mathematical expression you provided is difficult to read due to the low resolution of the image, but here is what it seems to be: √(x+7) - √(x-2) = √(x+2) - √(x-2) - (5/2) To solve for x, one would typically isolate the square roots on one side and then square both sides to eliminate the square root terms. However, there seems to be a mistake, because both sides of the equation contain the term √(x-2), which would cancel out. If this is correct, the equation after canceling the √(x-2) terms would simplify to: √(x+7) = √(x+2) - (5/2) Now let's proceed with this corrected equation. First, isolate the square root on one side: √(x+7) + (5/2) = √(x+2) Then square both sides to get rid of the square roots: (√(x+7) + 5/2)^2 = (√(x+2))^2 Expand the left-hand side: (x+7) + 2*(5/2)*√(x+7) + (5/2)^2 = x + 2 Simplify further by squaring (5/2) and combining like terms: x + 7 + 5√(x+7) + 25/4 = x + 2 Now, isolate the square root term: 5√(x+7) = x + 2 - (x + 7) - 25/4 5√(x+7) = -5 - 25/4 Since we cannot have a square root equal to a negative number (when considering real numbers), it seems there is no solution to the equation in the real number system. Please check the original equation to ensure it has been transcribed correctly. If there is a different equation, please provide a clearer image or the correct terms.
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