Can someone help me solve this equation?/
[SQRT(2x2 + 5x + 6)]=x
Square both sides:
2x^2 + 5x + 6 = x^2
x^2 + 5x + 6 = 0
(x+2)(x+3) = 0
x = -2 or x=-3
BUT, since we squared, all answers must be verified in the original equation
Neither works, so there is no solution.
had your equation been
√(2x2 - 5x + 6)]=x
the solution would have been
x = 2 or x=3 and both of those would have verified.
Thank you.
Also can you show me how I would do this equation??
2[SQRT(x + 4)] = 3
same way
square both sides
4(x+4) = 9
4x+16 = 9
4x = -7
x = -7/4
when verifying it worked.
Of course! To solve the equation [SQRT(2x^2 + 5x + 6)] = x, we can follow these steps:
Step 1: Square both sides of the equation to eliminate the square root:
[SQRT(2x^2 + 5x + 6)]^2 = x^2
Step 2: Simplify the left side of the equation. Squaring the square root cancels out the square root:
2x^2 + 5x + 6 = x^2
Step 3: Move all terms to one side of the equation to set it equal to zero:
2x^2 + 5x + 6 - x^2 = 0
Step 4: Combine like terms on the left side of the equation:
x^2 + 5x + 6 = 0
Step 5: Factor the quadratic equation:
(x + 2)(x + 3) = 0
Step 6: Set each factor equal to zero and solve for x:
x + 2 = 0 or x + 3 = 0
Solving for x in each equation:
x = -2 or x = -3
Therefore, the solutions to the equation [SQRT(2x^2 + 5x + 6)] = x are x = -2 and x = -3.