(x+1)² + (x-8)²=45 Rational Algebraic EQ​

Answer:(x+1)²+(x-8)²=45 are X = 2 and X = 5Step-by-step explanation:1. **Expand Each Term:** - When you expand the square of the sum of \(x\) and one, you get \(x\) squared plus two times \(x\) plus one. - When you expand the square of the difference between \(x\) and eight, you get \(x\) squared minus sixteen times \(x\) plus sixty-four.2. **Combine the Expanded Terms:** - Add the results from the expansions together. You get two times \(x\) squared minus fourteen times \(x\) plus sixty-five.3. **Subtract forty-five from this sum:** - This simplifies to two times \(x\) squared minus fourteen times \(x\) plus twenty.4. **Divide through by two to simplify:** - The result is \(x\) squared minus seven times \(x\) plus ten.5. **Factor this expression:** - This can be factored into the product of two binomials: one where \(x\) is subtracted by two and another where \(x\) is subtracted by five.6. **Solve for \(x\):** - Set each binomial equal to zero to find that \(x\) equals two or five.So, the solutions to the equation are \(x\) equal to two and \(x\) equal to five.

Answered by mimloverhorrorstory | 2024-09-04