Question

Calculate the expression: 14 - 3(2³ - 3 * 2) / [8 - 2((3 - x)² - 3 - (-2)²)]. Please provide the result of the calculation.

Answer 1

The result of the calculation is 3x² - 6x - 2.

Step-by-step explanation:

To calculate the expression: 14 - 3(2³ - 3 * 2) / [8 - 2((3 - x)² - 3 - (-2)²)], we need to follow the order of operations, also known as PEMDAS.

Step 1: Solve the expression inside the parentheses: 2³ - 3 * 2 = 8 - 6 = 2.

Step 2: Solve the expression inside the brackets: (3 - x)² - 3 - (-2)² = (3 - x)² - 3 - 4 = (3 - x)² - 7.

Step 3: Substitute the values we found into the original expression: 14 - 3(2) / [8 - 2((3 - x)² - 7)].

Step 4: Simplify the expression: 14 - 6 / [8 - 2(2 - x)² + 7].

Step 5: Solve the expression inside the parentheses: 2 - x = 2 - x.

Step 6: Substitute the simplified expression back into the original expression: 14 - 6 / [8 - 2(2 - x)² + 7].

Step 7: Combine like terms and solve the expression: 14 - 6 / [8 - 2(2 - x)² + 7] = 14 - 6 / [15 - 2(2 - x)²].

Step 8: Continue simplifying the expression: 14 - 6 / [15 - 2(4 - 2x + x²)].

Step 9: Simplify the expression inside the parentheses: 4 - 2x + x² = x² - 2x + 4.

Step 10: Substitute the simplified expression back into the original expression: 14 - 6 / [15 - 2(x² - 2x + 4)].

Step 11: Distribute the negative sign inside the brackets: 14 - 6 / [15 - 2x² + 4x - 8].

Step 12: Combine like terms and solve the expression: 14 - 6 / [-2x² + 4x + 11].

Step 13: Divide 6 by -2 to get -3 and simplify the expression: 14 - (-3x² + 6x + 16) /.

Step 14: Combine like terms and simplify the expression: 14 + 3x² - 6x - 16.

Step 15: Add the terms together to get the final result: 3x² - 6x - 2.