Solve by taking square roots or factoring.
2x^2=11x-12x
2x^2 = 11x - 12x = -x
Don't see how this can be solved. Typos?
2x^2 = - x
2x^2 + x = 0
x(2x + 1) = 0
x = 0
2x + 1 = 0 ... x = - 1/2
To solve the equation 2x^2 = 11x - 12x by taking square roots or factoring, we need to rearrange the equation so that one side equals zero.
First, combine the like terms on the right side of the equation:
2x^2 = 11x - 12x
2x^2 = -x
Next, bring all terms to one side to form a quadratic equation:
2x^2 + x = 0
Now, we can solve this equation by either taking square roots or factoring.
To solve by taking square roots:
1. Divide the equation by 2 to make the coefficient of x^2 equal to 1:
(2x^2 + x) / 2 = 0
x^2 + (1/2)x = 0
2. Take the square root of both sides of the equation:
sqrt(x^2 + (1/2)x) = sqrt(0)
x + (1/2) = 0 or x - (1/2) = 0
3. Solve for x by subtracting (1/2) from both sides:
x = -1/2 or x = 1/2
Therefore, the solutions to the equation 2x^2 = 11x - 12x by taking square roots are x = -1/2 or x = 1/2.
To solve by factoring:
1. Rearrange the equation in the standard form ax^2 + bx + c = 0, where a = 2, b = 1, and c = 0:
2x^2 + x = 0
2. Factor out the greatest common factor, which is x:
x(2x + 1) = 0
3. Apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero:
x = 0 or 2x + 1 = 0
4. Solve for x in each equation:
x = 0 or 2x = -1
x = 0 or x = -1/2
Therefore, the solutions to the equation 2x^2 = 11x - 12x by factoring are x = 0 or x = -1/2.