Evaluate the expression: x + x2 - 56

Mathematics
Evaluate the expression: x + x2 - 56

ScanSolve AI Answer

Answer

x=3,\ 4

Step 1: Factor the quadratic equation.

x27x+12=0x^2 - 7x + 12 = 0

Find two numbers that multiply to 12 and add to -7: -3 and -4.

x27x+12=(x3)(x4)=0x^2 - 7x + 12 = (x - 3)(x - 4) = 0

Step 2: Set each factor equal to zero.

x3=0x=3x - 3 = 0 \quad \Rightarrow \quad x = 3

x4=0x=4x - 4 = 0 \quad \Rightarrow \quad x = 4

The roots are x=3x = 3 and x=4x = 4.

x=3,\ 4

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Quick Answer
  1. x^2 - 7x + 12 = 0 Find two numbers that multiply to 12 and add to -7: -3 and -4.
  2. x^2 - 7x + 12 = (x - 3)(x - 4) = 0 Step 2: Set each factor equal to zero.
  3. x - 3 = 0 x = 3 x - 4 = 0 x = 4 The roots are x = 3 and x = 4.
Evaluate the expression: x + x2 - 56
Mathematics

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
Step 1: Factor the quadratic equation. x^2 - 7x + 12 = 0 Find two numbers that multiply to 12 and add to -7: -3 and -4. x^2 - 7x + 12 = (x - 3)(x - 4) = 0 Step 2: Set each factor equal to zero. x - 3 = 0 x = 3 x - 4 = 0 x = 4 The roots are x = 3 and x = 4. x=3,\ 4