Solve the quadratic by factoring. x^(2)-3x=4x-6 Answer: x=

Write Standard Form: Write the quadratic equation in standard form. To solve the quadratic equation by factoring, we need to write it in the standard form ax^2 + bx + c = 0. We do this by moving all terms to one side of the equation. x^2 - 3x - (4x - 6) = 0 x^2 - 3x - 4x + 6 = 0 Combine like terms. x^2 - 7x + 6 = 0Factor Quadratic Equation: Factor the quadratic equation. We need to find two numbers that multiply to give the constant term (c = 6) and add to give the coefficient of the x term (b = -7). The numbers that satisfy this are -1 and -6 because: (-1) * (-6) = 6 (-1) + (-6) = -7 So we can factor the quadratic as: (x - 1)(x - 6) = 0Solve Using Factored Form: Solve for x using the factored form. Set each factor equal to zero and solve for x. x - 1 = 0 or x - 6 = 0 x = 1 or x = 6 These are the solutions to the quadratic equation.

Home

Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Solve the quadratic by factoring.

\newline

x^{2}-3 x=4 x-6

\newline

Answer:

x=

Write Standard Form: Write the quadratic equation in standard form. $\newline$ To solve the quadratic equation by factoring, we need to write it in the standard form $ax^2 + bx + c = 0$ . We do this by moving all terms to one side of the equation. $\newline$ $x^2 - 3x - (4x - 6) = 0$ $\newline$ $x^2 - 3x - 4x + 6 = 0$ $\newline$ Combine like terms. $\newline$ $x^2 - 7x + 6 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to give the constant term $c = 6$ and add to give the coefficient of the $x$ term $b = -7$ . $\newline$ The numbers that satisfy this are $-1$ and $-6$ because: $\newline$ $(-1) \times (-6) = 6$ $\newline$ $(-1) + (-6) = -7$ $\newline$ So we can factor the quadratic as: $\newline$ $(x - 1)(x - 6) = 0$
Solve Using Factored Form: Solve for $x$ using the factored form. $\newline$ Set each factor equal to zero and solve for $x$ . $\newline$ $x - 1 = 0$ or $x - 6 = 0$ $\newline$ $x = 1$ or $x = 6$ $\newline$ These are the solutions to the quadratic equation.