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: $x=\frac{-bpmsqrt{b^{2}-4ac}}{2a}$\n$x=\frac{-(-2)pmsqrt{(-2)^{2}-4(3)(0)}}{2(3)}$\n$x=\frac{-(-2)pmsqrt{(-2)^{2}-4(3)(2)}}{2(3)}$\n$x=\frac{-(-2)pmsqrt{(-2)^{2}-4(3)(1)}}{2(3)}$\n$x=\frac{-3pmsqrt{3^{2}-4(-2)(0)}}{2(-2)}$

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: $x=\frac{-bpmsqrt{b^{2}-4ac}}{2a}$\n$x=\frac{-(-2)pmsqrt{(-2)^{2}-4(3)(0)}}{2(3)}$\n$x=\frac{-(-2)pmsqrt{(-2)^{2}-4(3)(2)}}{2(3)}$\n$x=\frac{-(-2)pmsqrt{(-2)^{2}-4(3)(1)}}{2(3)}$\n$x=\frac{-3pmsqrt{3^{2}-4(-2)(0)}}{2(-2)}$

Answer

Explanation:

Step1: Rewrite the equation in standard form

The standard - form of a quadratic equation is $ax^{2}+bx + c = 0$. Given $1=-2x + 3x^{2}+1$, we can rewrite it as $3x^{2}-2x+1 - 1=0$, which simplifies to $3x^{2}-2x+0 = 0$. So, $a = 3$, $b=-2$, and $c = 0$.

Step2: Substitute values into quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substituting $a = 3$, $b=-2$, and $c = 0$ gives $x=\frac{-(-2)\pm\sqrt{(-2)^{2}-4(3)(0)}}{2(3)}$.

Answer:

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