Explain why the equation (x-3)^2-38=11 has two solutions. Then solve the equation to find the solutions. Show your work.
1 answer:
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Refer to the diagram shown below.
Because ΔABC is isosceles and AB = AC, therefore
m∠C = m∠B = (3x + 5)°
The sum of angles in a triangle is 180°, therefore
2(3x + 5) + 2x - 20 = 180
6x + 10 + 2x - 20 = 180
8x - 10 = 180
8x = 190
x = 23.75°
Therefore
m∠C = 3x + 5 = 3(23.75) + 5 = 76.25°
Answer: 76.25°
Because ΔABC is isosceles and AB = AC, therefore
m∠C = m∠B = (3x + 5)°
The sum of angles in a triangle is 180°, therefore
2(3x + 5) + 2x - 20 = 180
6x + 10 + 2x - 20 = 180
8x - 10 = 180
8x = 190
x = 23.75°
Therefore
m∠C = 3x + 5 = 3(23.75) + 5 = 76.25°
Answer: 76.25°