which shows the correct substitution of the values a, b, and c from the equation 1 = -2x + 3x² + 1 into the…

which shows the correct substitution of the values a, b, and c from the equation 1 = -2x + 3x² + 1 into the quadratic formula?\nquadratic formula: x = \\frac{-b\\pm\\sqrt{b^{2}-4ac}}{2a}\n\\(x = \\frac{-(-2)\\pm\\sqrt{(-2)^{2}-4(3)(0)}}{2(3)}\\)\n\\(x = \\frac{-(-2)\\pm\\sqrt{(-2)^{2}-4(3)(2)}}{2(3)}\\)\n\\(x = \\frac{-(-2)\\pm\\sqrt{(-2)^{2}-4(3)(1)}}{2(3)}\\)\n\\(x = \\frac{-3\\pm\\sqrt{3^{2}-4(-2)(0)}}{2(-2)}\\)

which shows the correct substitution of the values a, b, and c from the equation 1 = -2x + 3x² + 1 into the quadratic formula?\nquadratic formula: x = \\frac{-b\\pm\\sqrt{b^{2}-4ac}}{2a}\n\\(x = \\frac{-(-2)\\pm\\sqrt{(-2)^{2}-4(3)(0)}}{2(3)}\\)\n\\(x = \\frac{-(-2)\\pm\\sqrt{(-2)^{2}-4(3)(2)}}{2(3)}\\)\n\\(x = \\frac{-(-2)\\pm\\sqrt{(-2)^{2}-4(3)(1)}}{2(3)}\\)\n\\(x = \\frac{-3\\pm\\sqrt{3^{2}-4(-2)(0)}}{2(-2)}\\)

Answer

Explanation:

Step1: Rearrange the equation

First, rewrite the equation $1=-2x + 3x^{2}+1$ in standard quadratic - form $ax^{2}+bx + c = 0$. Subtract 1 from both sides to get $3x^{2}-2x+1 - 1=0$, which simplifies to $3x^{2}-2x=0$. So, $a = 3$, $b=-2$, and $c = 0$.

Step2: Substitute into quadratic formula

Substitute $a = 3$, $b=-2$, and $c = 0$ into the quadratic formula $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. We get $x=\frac{-(-2)\pm\sqrt{(-2)^{2}-4(3)(0)}}{2(3)}$.

Answer:

$x=\frac{-(-2)\pm\sqrt{(-2)^{2}-4(3)(0)}}{2(3)}$