This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — here are the solutions for solving for x: a) Step 1: Set the quadratic expression equal to zero. x^2 - 4x + 3 = 0 Step 2: Factor the quadratic expression. We need two numbers that multiply to 3 and add to -4. These numbers are -1 and -3. (x-1)(x-3) = 0 Step 3: Set each factor equal to zero and solve for x. x-1=0 or x-3=0 x=1 or x=3 x=1 or x=3 b) Step 1: Set the quadratic expression equal to zero. x^2 - 7x + 6 = 0 Step 2: Factor the quadratic expression. We need two numbers that multiply to 6 and add to -7. These numbers are -1 and -6. (x-1)(x-6) = 0 Step 3: Set each factor equal to zero and solve for x. x-1=0 or x-6=0 x=1 or x=6 x=1 or x=6 c) Step 1: Set the quadratic expression equal to zero. x^2 + 4x + 3 = 0 Step 2: Factor the quadratic expression. We need two numbers that multiply to 3 and add to 4. These numbers are 1 and 3. (x+1)(x+3) = 0 Step 3: Set each factor equal to zero and solve for x. x+1=0 or x+3=0 x=-1 or x=-3 x=-1 or x=-3 d) Step 1: Set the quadratic expression equal to zero. x^2 + 4x + 4 = 0 Step 2: Factor the quadratic expression. This is a perfect square trinomial. We need two numbers that multiply to 4 and add to 4. These numbers are 2 and 2. (x+2)(x+2) = 0 (x+2)^2 = 0 Step 3: Set the factor equal to zero and solve for x. x+2=0 x=-2 x=-2 e) Step 1: Set the expression equal to zero. x^2 - 16 = 0 Step 2: Factor the expression using the difference of squares formula (a^2 - b^2 = (a-b)(a+b)). Here, a=x and b=4. (x-4)(x+4) = 0 Step 3: Set each factor equal to zero and solve for x. x-4=0 or x+4=0 x=4 or x=-4 x=4 or x=-4 Drop the next question.