Final answer:
The two equations given can be expanded and terms combined to rewrite them in the standard quadratic form ax^2 + bx + c = 0. The first becomes -5x^2 - 34x + 22 = 0 and the second is -2x^2 - 2x - 5 = 0. The quadratic formula can then be applied to solve for x.
Step-by-step explanation:
To rewrite the given equations in the standard form ax^2 + bx + c = 0, we need to expand and combine like terms and move all terms to one side of the equation to set it equal to zero.
The first equation is:
-5x(x + 6) = 4(x - 3) - 10.
Expanding both sides we get:
-5x^2 - 30x = 4x - 12 - 10.
Now, bring all terms to one side:
-5x^2 - 30x - 4x + 12 + 10 = 0.
Combine like terms:
-5x^2 - 34x + 22 = 0.
The second equation is:
4x^2 - 2x(3x + 1) = 5.
Expanding the left side we get:
4x^2 - 6x^2 - 2x = 5.
Combine like terms and subtract 5 from both sides:
-2x^2 - 2x - 5 = 0.
The rewritten equations in the standard form are:
-5x^2 - 34x + 22 = 0 and -2x^2 - 2x - 5 = 0.
Solving these equations can be done using the quadratic formula, which is useful for equations in this standard form.