Answer:
Explanation:
To find the value of X for the given quadratic equation, we will use three different methods: factorization, completing the square, and the quadratic formula.
i) Factorization:
To factorize the quadratic equation, we need to express it as a product of two binomials. Let's assume the equation is in the form ax^2 + bx + c = 0.
Step 1: Rewrite the equation in the form ax^2 + bx + c = 0.
Step 2: Identify two numbers whose sum is equal to the coefficient of the middle term (bx) and whose product is equal to the product of the coefficient of the squared term (ax^2) and the constant term (c).
Step 3: Rewrite the middle term (bx) using the two numbers found in step 2.
Step 4: Factorize the quadratic equation by grouping terms and factoring out common factors.
Step 5: Set each factor equal to zero and solve for x.
ii) Completing the Square Method:
Completing the square is a method used to solve quadratic equations by transforming them into a perfect square trinomial.
Step 1: Rewrite the equation in the form ax^2 + bx + c = 0.
Step 2: Divide the equation by the coefficient of the squared term (a), if necessary, to make it equal to 1.
Step 3: Move the constant term (c) to the right side of the equation.
Step 4: Take half of the coefficient of the middle term (b/2) and square it. Add this value to both sides of the equation.
Step 5: Rewrite the left side of the equation as a perfect square trinomial.
Step 6: Solve the equation by taking the square root of both sides and isolating x.
iii) Quadratic Formula:
The quadratic formula is a general formula used to solve quadratic equations of the form ax^2 + bx + c = 0.
The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / 2a
Step 1: Identify the values of a, b, and c from the given equation.
Step 2: Substitute the values of a, b, and c into the quadratic formula.
Step 3: Simplify the equation by performing the necessary calculations.
Step 4: Solve for x by taking the positive and negative square roots and simplifying further if needed.
By using these three methods, we can find the value of X for the given quadratic equation. It is important to note that the specific equation and coefficients need to be provided in order to obtain the exact solution.