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(a-1)(a-2)+(a-3)(a+4)-(2a^2+5a-34)=-7a+24

2 min read Jun 16, 2024
(a-1)(a-2)+(a-3)(a+4)-(2a^2+5a-34)=-7a+24

Solving the Equation: (a-1)(a-2)+(a-3)(a+4)-(2a^2+5a-34)=-7a+24

This article will guide you through the steps of solving the given equation.

Expanding the Equation

The first step is to expand the equation by multiplying out the brackets and combining like terms.

  1. Expand (a-1)(a-2): (a-1)(a-2) = a² - 2a - a + 2 = a² - 3a + 2

  2. Expand (a-3)(a+4): (a-3)(a+4) = a² + 4a - 3a - 12 = a² + a - 12

  3. Rewrite the equation: a² - 3a + 2 + a² + a - 12 - (2a² + 5a - 34) = -7a + 24

  4. Simplify the left side: 2a² - 7a + 24 - 2a² - 5a + 34 = -7a + 24

  5. Combine like terms: -12a + 58 = -7a + 24

Solving for 'a'

Now we have a simpler equation with only one variable. Let's solve for 'a'.

  1. Add 7a to both sides: -5a + 58 = 24

  2. Subtract 58 from both sides: -5a = -34

  3. Divide both sides by -5: a = 6.8

Conclusion

Therefore, the solution to the equation (a-1)(a-2)+(a-3)(a+4)-(2a^2+5a-34)=-7a+24 is a = 6.8.

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