Solve for x. Enter the solutions from least to greatest. {:[2x^(2)-24 x+54=0],[" lesser "x=◻],[" greater "x=◻]:}

Question

Solve for  x. Enter the solutions from least to greatest.  {:[2x^(2)-24 x+54=0],[" lesser "x=◻],[" greater "x=◻]:}

Bytelearn · Accepted Answer

Write quadratic equation: Write down the quadratic equation. We have the quadratic equation 2x^2 - 24x + 54 = 0.Factor quadratic equation: Factor the quadratic equation. To factor the quadratic equation, we need to find two numbers that multiply to give the product of the coefficient of x^2 (which is 2) and the constant term (which is 54), and add up to the coefficient of x (which is -24). The product of the coefficient of x^2 and the constant term is 2 * 54 = 108. We need two numbers that multiply to 108 and add up to -24. The numbers -12 and -9 satisfy these conditions because -12 * -9 = 108 and -12 + -9 = -24.Rewrite using found numbers: Rewrite the quadratic equation using the numbers found. We can rewrite the middle term -24x using the numbers -12 and -9. 2x^2 - 24x + 54 = 2x^2 - 12x - 9x + 54Factor by grouping: Factor by grouping. Now we group the terms to factor by grouping: (2x^2 - 12x) + (-9x + 54) = 0 We can factor out a common factor of 2x from the first group and -9 from the second group: 2x(x - 6) - 9(x - 6) = 0Factor out common binomial: Factor out the common binomial factor. We notice that (x - 6) is a common factor: (2x - 9)(x - 6) = 0Solve for x: Solve for x using the zero product property. We set each factor equal to zero and solve for x: 2x - 9 = 0 or x - 6 = 0 For 2x - 9 = 0, add 9 to both sides to get 2x = 9, then divide by 2 to get x = 9/2. For x - 6 = 0, add 6 to both sides to get x = 6.Write solutions in ascending order: Write the solutions in ascending order. The solutions are x = 9/2 and x = 6. In ascending order, we have x = 9/2, x = 6.

Solve for $x$ . Enter the solutions from least to greatest. $\newline$ $2 x^{2}-24 x+54=0$ $\newline$ lesser $x=$ $\newline$ greater $x=$

Full solution

More problems from Solve a quadratic equation by factoring

Related topics

Solve for x x x. Enter the solutions from least to greatest.\newline2x2−24x+54=0 2 x^{2}-24 x+54=0 2x2−24x+54=0\newlinelesser x= x= x=\newlinegreater x= x= x=

Solve for $x$ . Enter the solutions from least to greatest. $\newline$ $2 x^{2}-24 x+54=0$ $\newline$ lesser $x=$ $\newline$ greater $x=$