Solve and check. Show complete working.a. w2 − 18w + 56 = 0b. x2 − 2x = 0

a. To solve the quadratic equation w² - 18w + 56 = 0, we can use the quadratic formula, which is w = [-b ± sqrt(b² - 4ac)] / 2a. Here, a = 1, b = -18, and c = 56.

Step 1: Calculate the discriminant, which is b² - 4ac = (-18)² - 4156 = 324 - 224 = 100.

Step 2: Substitute a, b, and the discriminant into the quadratic formula to find the solutions.

w = [18 ± sqrt(100)] / 2*1 w = [18 ± 10] / 2 w = 28 / 2 or w = 8 / 2 w = 14 or w = 4

So, the solutions are w = 14 and w = 4.

To check the solutions, substitute w = 14 and w = 4 into the original equation:

For w = 14: 14² - 1814 + 56 = 196 - 252 + 56 = 0 For w = 4: 4² - 184 + 56 = 16 - 72 + 56 = 0

So, the solutions are correct.

b. To solve the equation x² - 2x = 0, we can factor the equation.

Step 1: Factor the equation: x(x - 2) = 0

Step 2: Set each factor equal to zero and solve for x: x = 0 and x - 2 = 0, which gives x = 0 and x = 2.

So, the solutions are x = 0 and x = 2.

To check the solutions, substitute x = 0 and x = 2 into the original equation:

For x = 0: 0² - 20 = 0 For x = 2: 2² - 22 = 0

So, the solutions are correct.