Final answer:
To rewrite the equation 4x² + 28x -2 =0 by completing the square, follow these steps: move the constant term to the right side of the equation, divide the coefficient of x² by 2 and square the result, add the result to both sides of the equation, rewrite the left side as a perfect square trinomial, and solve for x.
Step-by-step explanation:
To rewrite the equation 4x² + 28x -2 =0 by completing the square, we follow these steps:
Step 1: Move the constant term (-2) to the right side of the equation.
Step 2: Divide the coefficient of x² (4) by 2 and square the result. This gives us (4/2)² = 2² = 4.
Step 3: Add the result from step 2 to both sides of the equation.
Step 4: Rewrite the left side of the equation as a perfect square trinomial.
Step 5: Solve the resulting equation using the square root property or factoring.
So, by completing the square, the equation 4x² + 28x -2 = 0 can be rewritten as (2x + 7)² - 51 = 0.