Final answer:
To solve the equation with the expression (14x^2+12x-3), we can simplify the denominator and write it as a perfect square. By recognizing that the left side of the equation is a perfect square, we can solve for x easily. For quadratic equations with an x² term, there will be two possible values for the unknown x. Completing the square in x² can help simplify the equation.
Step-by-step explanation:
This is an equation in one variable, so we should be able to solve for the unknown value. This expression may look formidable, but first we can simplify the denominator and write it as a perfect square as well:
- We could solve this equation with the quadratic formula, but it is far easier to solve for x by recognizing that the left side of the equation is a perfect square; that is,
- Sometimes when an ICE chart is set up and the Keq expression is constructed, a more complex algebraic equation will result. One of the more common equations has an x² term in it and is called a quadratic equation. There will be two values possible for the unknown x, and for a quadratic equation with the general formula ax² + bx + c = 0 (where a, b, and c are the coefficients of the quadratic equation), the two possible values are as follows:
- If we complete the square in x², this condition simplifies to 2 (x² − ¹)² ≤ which we can solve to obtain