4x^2-5x-15=0

Simple and best practice solution for 4x^2-5x-15=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 4x^2-5x-15=0 equation:


Simplifying
4x2 + -5x + -15 = 0

Reorder the terms:
-15 + -5x + 4x2 = 0

Solving
-15 + -5x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-3.75 + -1.25x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -1.25x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -1.25x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -1.25x + x2 = 0 + 3.75
-1.25x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-1.25x + x2 = 3.75

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = 3.75 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = 3.75 + 0.390625

Combine like terms: 3.75 + 0.390625 = 4.140625
0.390625 + -1.25x + x2 = 4.140625

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 4.140625

Calculate the square root of the right side: 2.034852575

Break this problem into two subproblems by setting 
(x + -0.625) equal to 2.034852575 and -2.034852575.

Subproblem 1

x + -0.625 = 2.034852575 Simplifying x + -0.625 = 2.034852575 Reorder the terms: -0.625 + x = 2.034852575 Solving -0.625 + x = 2.034852575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 2.034852575 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 2.034852575 + 0.625 x = 2.034852575 + 0.625 Combine like terms: 2.034852575 + 0.625 = 2.659852575 x = 2.659852575 Simplifying x = 2.659852575

Subproblem 2

x + -0.625 = -2.034852575 Simplifying x + -0.625 = -2.034852575 Reorder the terms: -0.625 + x = -2.034852575 Solving -0.625 + x = -2.034852575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -2.034852575 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -2.034852575 + 0.625 x = -2.034852575 + 0.625 Combine like terms: -2.034852575 + 0.625 = -1.409852575 x = -1.409852575 Simplifying x = -1.409852575

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.659852575, -1.409852575}

See similar equations:

| 22=6d+2 | | 5=e^2k | | 30+75w+x=180 | | 7x-11-3x=10x-2(3x+5)+6 | | 5(x^2+4)-3=4(x^2-2x)+26 | | 5x^3-7x^2-25x=0 | | 19=2h+5 | | x+(x-15)=65 | | 19=5x+2 | | 10=2e^2k | | -5y-11=2y+17 | | x-7y=20solvey | | 0.80a-0.50a+10=5.2 | | 4x+7=-7+2x+24 | | 6x-6=6(x-2) | | 16+8w-w=2 | | -4g-6g+1=51 | | 8+4m=9m+23 | | x^2+9x+18=27+2x^2+6x | | 15-14x=10x+9 | | 12b-3=10b+9 | | 3x+2y=62 | | 15-14x=-10+9 | | u^2+9u-14=0 | | -220=5(8b-4) | | 1.2m-6=42 | | -x-9=11 | | 4x+4y=3y-5 | | 2(x-4)=3(x-2)+1 | | 3x^3-3x-6=12 | | X*X-7+4x+5=90 | | 250=(2x+5) |

Equations solver categories