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Factoring quadratic equations is a method used to break down the equation into simpler expressions. A quadratic equation is typically in the form of \(ax^2 + bx + c = 0\), where \a\, \b\, and \c\ are constants. In the equation provided, \(x^2 + 4x - 60 = 0\), \a = 1\, \b = 4\, and \c = -60\.

To factor this equation, we look for two numbers that multiply to \-60\ and add up to \4\. In this case, those numbers are \10\ and \-6\ because \10 \times (-6) = -60\ and \10 + (-6) = 4\.

Once these numbers are found, the equation can be written in its factored form as: \ (x + 10)(x - 6) = 0 \. Factoring helps to simplify the equation and make it easier to find the solutions.

Setting the equation to zero is a crucial step in solving quadratic equations. This involves moving all terms to one side of the equation to ensure the right side equals zero.

For the exercise provided, the original equation is \(x^2 + 4x = 60\). The constant term \60\ is moved to the left side by subtracting it from both sides, resulting in \(x^2 + 4x - 60 = 0\).

Having the equation set to zero is essential for the factoring method to work, as it allows us to find the points where the expression equals zero, leading to the solutions of the quadratic equation.

This process turns the equation into a format that is more straightforward to solve.

Finding the roots of a quadratic equation means determining the values of \x\ that satisfy the equation. After factoring the quadratic equation and setting it to zero, the next step is to find the values of \x\ that make each factor zero.

In the provided example, we have: \ (x + 10)(x - 6) = 0 \. To find the roots, set each factor equal to zero:
- \(x + 10 = 0\), solving this gives \(x = -10\).
- \(x - 6 = 0\), solving this gives \(x = 6\).

Therefore, the roots of the quadratic equation \(x^2 + 4x - 60 = 0\) are \-10\ and \6\.

These values are also known as the solutions, zeros, or x-intercepts of the equation. Finding roots is the ultimate goal when solving quadratic equations, as it provides the values at which the quadratic expression equals zero.