Solve the quadratic equation:

\[ x^2 + 6x + 5 = 45 \]

First bring all terms to one side left equal to zero X^2 + 6x - 40 Now we need to factor this, meaning find 2 binomials that when multiplied result in the original. Start with (x )(x ) because x*x= x^2 The last part is negative, so we can turn it into (x+ )(x- ) Now we need to find two numbers that add to 6 and multiply to -40 The numbers that work are 10 and -4 Now we put those in to get (x+10)(x-4)=0 Now it is factored. Because they equal 0, that means that one or both of the expressions inside the parentheses must equal zero So we can split it up into x+10=0 and x-4=0 Solving for those we get x=-10 or x=4 Final answer: X=-10 or x=4

Answered by FirstSineOfMadness | 2024-06-10

To solve the quadratic equation x² + 6x + 5 = 45, we first rearranged it to x² + 6x - 40 = 0. By factoring, we found the solutions to be x = -10 and x = 4. Thus, these are the values that satisfy the equation.
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Answered by FirstSineOfMadness | 2024-12-26