Solve for all values of x : x^(2)(4x-1)+x(4x-1)-20(4x-1)=0 Answer: x=

Factor Out Common Term: Factor out the common term (4x-1) from each part of the equation. x^2(4x-1) + x(4x-1) - 20(4x-1) = 0 (4x-1)(x^2 + x - 20) = 0Solve for Common Factor: Set each factor equal to zero and solve for x. First, set the common factor (4x-1) equal to zero: 4x - 1 = 0 4x = 1 x = 1/4Factor and Solve Quadratic: Now, set the quadratic factor (x^2 + x - 20) equal to zero and solve for x. x^2 + x - 20 = 0 To solve this quadratic equation, we can factor it. (x + 5)(x - 4) = 0Solve for Quadratic Factors: Set each factor of the quadratic equation equal to zero and solve for x. x + 5 = 0 x = -5 x - 4 = 0 x = 4

Home

Math Problems

Grade 8

Solve multi-step equations

Full solution

Q. Solve for all values of

x

\newline

x^{2}(4 x-1)+x(4 x-1)-20(4 x-1)=0

\newline

Answer:

x=

Factor Out Common Term: Factor out the common term $(4x-1)$ from each part of the equation. $\newline$ $x^2(4x-1) + x(4x-1) - 20(4x-1) = 0$ $\newline$ $(4x-1)(x^2 + x - 20) = 0$
Solve for Common Factor: Set each factor equal to zero and solve for $x$ . $\newline$ First, set the common factor $4x-1$ equal to zero: $\newline$ $4x - 1 = 0$ $\newline$ $4x = 1$ $\newline$ $x = \frac{1}{4}$
Factor and Solve Quadratic: Now, set the quadratic factor $x^2 + x - 20$ equal to zero and solve for $x$ . $x^2 + x - 20 = 0$ To solve this quadratic equation, we can factor it. $(x + 5)(x - 4) = 0$
Solve for Quadratic Factors: Set each factor of the quadratic equation equal to zero and solve for $x$ . $x + 5 = 0$ $x = -5$ $x - 4 = 0$ $x = 4$