How do you solve #4x^2-4x=15#?

Question

Avery Alexander · Accepted Answer

#x_1=5/2# or #x_2=-3/2# Writing your equation in the form #4x^2-4x-15=0# dividing by #4# #x^2-x-15/4=0# using the quadratic formula #x_{1,2}=1/2pmsqrt(1/4+15/4)# so we get #x_1=5/2# #x_2=-3/2#

Avery Alexander · Answer

#x=-3/2" or "x=5/2# #"rearrange in standard form ";ax^2+bx+c=0# #"subtract 15 from both sides"# #4x^2-4x-15=0# #"using the a-c method to factor the quadratic"# #"the factors of the product "4xx-15=-60# #"which sum to - 4 are + 6 and - 10"# #"split the middle term using these factors"# #4x^2+6x-10x-15=0larrcolor(blue)"factor by grouping"# #color(red)(2x)(2x+3)color(red)(-5)(2x+3)=0# #"take out the "color(blue)"common factor "(2x+3)# #(2x+3)(color(red)(2x-5))=0# #"equate each factor to zero and solve for x"# #2x+3=0rArrx=-3/2# #2x-5=0rArrx=5/2#

Jace Anderson · Answer

undefined To solve the equation 4x^2 - 4x = 15, you can follow these steps:

1. Move all terms to one side of the equation to set it equal to zero: 4x^2 - 4x - 15 = 0.

2. Factor the quadratic equation or use the quadratic formula to find the roots.

3. If factoring is possible, factor the quadratic expression. If not, apply the quadratic formula.

4. Apply the quadratic formula, which states that for the quadratic equation ax^2 + bx + c = 0, the solutions are given by x = (-b ± √(b^2 - 4ac)) / (2a).

5. Substitute the values of a, b, and c from the given equation into the quadratic formula.

6. Solve for x by performing the necessary arithmetic operations.

7. Once you have found the values of x, check your solutions by substituting them back into the original equation to ensure they satisfy the equation.

By following these steps, you can find the solutions to the equation 4x^2 - 4x = 15.