Solve for g. g^2 - 10g + 21 = 0 Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. g = ____

Question

Solve for g. g^2 - 10g + 21 = 0   Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. g = ____

Bytelearn · Accepted Answer

Identify values: Identify the values of a, b, and c in the quadratic equation g^2 - 10g + 21 = 0, which are a = 1, b = -10, and c = 21.Find numbers: Look for two numbers that multiply to ac (which is 1*21 = 21) and add up to b (which is -10). The numbers that satisfy these conditions are -3 and -7 because -3*-7 = 21 and -3 + -7 = -10.Write factored form: Write the quadratic equation in its factored form using the numbers found in Step 2. Since g^2 - 10g + 21 factors into (g - 3)(g - 7), we can set each factor equal to zero to find the solutions for g.Set first factor: Set the first factor equal to zero: (g - 3) = 0. Solve for g by adding 3 to both sides of the equation to get g = 3.Set second factor: Set the second factor equal to zero: (g - 7) = 0. Solve for g by adding 7 to both sides of the equation to get g = 7.

Solve for $g$ . $\newline$ $g^2 - 10g + 21 = 0$ $\newline$ Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. $\newline$ $g = \_\_$

Full solution

More problems from Solve polynomial equations

Related topics

Solve for ggg. \newlineg2−10g+21=0g^2 - 10g + 21 = 0g2−10g+21=0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. \newlineg=__g = \_\_g=__

Solve for $g$ . $\newline$ $g^2 - 10g + 21 = 0$ $\newline$ Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. $\newline$ $g = \_\_$