zacharias is using the quadratic formula to solve the equation 0 = -2x² + 5x - 3. he begins by substituting…

Explanation:

Step1: Identify coefficients in quadratic equation

For the quadratic equation $0 = - 2x^{2}+5x - 3$, we have $a=-2$, $b = 5$, $c=-3$.

Step2: Recall quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.

Step3: Substitute coefficients correctly

When substituting $a=-2$, $b = 5$, $c=-3$ into the quadratic formula, we get $x=\frac{-5\pm\sqrt{5^{2}-4(-2)(-3)}}{2(-2)}$. The error is in the sign of the $-b$ term. Since $b = 5$, $-b=-5$ is correct. But looking at the substitution in the $b^{2}$ part, it should be based on the original $b$ value. The correct substitution for the discriminant part should be based on the original $b = 5$, so it should be $5^{2}$ (not $- 5^{2}$). The $a=-2$ is correctly used in the denominator as $2a = 2(-2)$. The error is that the $5^{2}$ should not be $-5^{2}$.

Answer:

The $5^{2}$ should be $-5^{2}$.