Solve for the variable in the following equaitons: \( 5 x-2 x+5=13+x \) \( \sqrt{6}-2(r+2)^{2}+5=-45 \)

We are given two equations to solve. ──────────────────────── 1) Solve 5x – 2x + 5 = 13 + x Step 1. Combine like terms on the left side:   5x – 2x = 3x,   so the equation becomes:   3x + 5 = 13 + x Step 2. Get all x terms on one side by subtracting x from both sides:   3x – x + 5 = 13   2x + 5 = 13 Step 3. Isolate 2x by subtracting 5 from both sides:   2x = 13 – 5   2x = 8 Step 4. Divide both sides by 2:   x = 8/2   x = 4 ──────────────────────── 2) Solve √6 – 2(r + 2)² + 5 = –45 Step 1. Combine the constant terms √6 and 5:   √6 + 5 – 2(r + 2)² = –45 Step 2. Isolate the squared term by subtracting (√6 + 5) from both sides:   –2(r + 2)² = –45 – (√6 + 5)   –2(r + 2)² = –45 – √6 – 5   –2(r + 2)² = –50 – √6 Step 3. Divide both sides by –2 (remembering to flip the sign):   (r + 2)² = (50 + √6) / 2 Step 4. Take the square root of both sides, remembering the ±:   r + 2 = ± √[(50 + √6) / 2] Step 5. Solve for r by subtracting 2:   r = –2 ± √[(50 + √6) / 2] ──────────────────────── Final Answers: 1) x = 4 2) r = –2 + √[(50 + √6) / 2]  or  r = –2 – √[(50 + √6) / 2]