How can I express the equation 6x^2 + 54x + 4x + 52 + 6 = 0 as a quadratic equation using substitution?

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To convert the expression 6x^2 + 54x + 4x + 52 + 6 = 0 into a standard quadratic form, we need to first combine like terms. Let’s break it down step by step:

  1. Combine the linear terms: 54x + 4x gives us 58x.
  2. Now, rewrite the equation as: 6x^2 + 58x + 52 + 6 = 0.
  3. Next, add 52 and 6 to get 58.
  4. Your equation now looks like: 6x^2 + 58x + 58 = 0.

Now, this is a quadratic equation in standard form, which is generally represented as ax² + bx + c = 0. Here, we have:

  • a = 6
  • b = 58
  • c = 58

To solve the quadratic equation, you may use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. Plug in the values:

x = (-58 ± √(58² - 4 * 6 * 58)) / (2 * 6).

This leads to x = (-58 ± √(3364 - 1392)) / 12.

Finally, simplify inside the square root:

x = (-58 ± √1972) / 12.

This is how you express and tackle the given expression in the format of a quadratic equation. If you have any further questions regarding quadratics, feel free to ask!

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