Question

Solve algebraically
2(x+1) ^2 -3= -5x +5

Answer 1

To solve the given equation algebraically, distribute the 2, expand the equation, combine like terms, and set the equation equal to zero. Then, factor or use the quadratic formula to find the values of x.

Step-by-step explanation:

To solve the equation 2(x+1)^2 - 3 = -5x + 5 algebraically, we need to simplify and rearrange the equation until we isolate x. Here are the steps:

1. Distribute the 2 to both terms inside the parentheses: 2(x^2 + 2x + 1) - 3 = -5x + 5
2. Expand the equation: 2x^2 + 4x + 2 - 3 = -5x + 5
3. Combine like terms: 2x^2 + 4x - 1 = -5x + 5
4. Add 5x to both sides: 2x^2 + 9x - 1 = 5
5. Set the equation equal to zero: 2x^2 + 9x - 6 = 0
6. Now, you can either factor the quadratic equation or use the quadratic formula to solve for x.