complete the equation so that it has solutions of -5 and 7.\nx² + x + = 0

Answer:

The first blank is $- 2$, the second blank is $-35$.

Explanation:

Step1: Recall the factored - form of a quadratic equation

If the solutions of a quadratic equation $ax^{2}+bx + c = 0$ are $x_1$ and $x_2$, then the equation can be written as $a(x - x_1)(x - x_2)=0$. Here $a = 1$, $x_1=-5$ and $x_2 = 7$. So the equation is $(x + 5)(x - 7)=0$.

Step2: Expand the factored - form

Using the FOIL method: $(x + 5)(x - 7)=x\times x+x\times(-7)+5\times x + 5\times(-7)$. $=x^{2}-7x + 5x-35$.

Step3: Simplify the expanded form

Combine like - terms: $x^{2}+(-7 + 5)x-35=x^{2}-2x-35 = 0$. So the coefficient of $x$ is $-2$ and the constant term is $-35$.