4x^2+6x-17=0

Simple and best practice solution for 4x^2+6x-17=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+6x-17=0 equation:


Simplifying
4x2 + 6x + -17 = 0

Reorder the terms:
-17 + 6x + 4x2 = 0

Solving
-17 + 6x + 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'.
-4.25 + 1.5x + x2 = 0

Move the constant term to the right:

Add '4.25' to each side of the equation.
-4.25 + 1.5x + 4.25 + x2 = 0 + 4.25

Reorder the terms:
-4.25 + 4.25 + 1.5x + x2 = 0 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + 1.5x + x2 = 0 + 4.25
1.5x + x2 = 0 + 4.25

Combine like terms: 0 + 4.25 = 4.25
1.5x + x2 = 4.25

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 4.25 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 4.25 + 0.5625

Combine like terms: 4.25 + 0.5625 = 4.8125
0.5625 + 1.5x + x2 = 4.8125

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 4.8125

Calculate the square root of the right side: 2.193741097

Break this problem into two subproblems by setting 
(x + 0.75) equal to 2.193741097 and -2.193741097.

Subproblem 1

x + 0.75 = 2.193741097 Simplifying x + 0.75 = 2.193741097 Reorder the terms: 0.75 + x = 2.193741097 Solving 0.75 + x = 2.193741097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.193741097 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.193741097 + -0.75 x = 2.193741097 + -0.75 Combine like terms: 2.193741097 + -0.75 = 1.443741097 x = 1.443741097 Simplifying x = 1.443741097

Subproblem 2

x + 0.75 = -2.193741097 Simplifying x + 0.75 = -2.193741097 Reorder the terms: 0.75 + x = -2.193741097 Solving 0.75 + x = -2.193741097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.193741097 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.193741097 + -0.75 x = -2.193741097 + -0.75 Combine like terms: -2.193741097 + -0.75 = -2.943741097 x = -2.943741097 Simplifying x = -2.943741097

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.443741097, -2.943741097}

See similar equations:

| 16=-6x-3 | | (x-1/3)(x+1/3) | | 2(w+7)(w-3)=w^2+7w+68 | | 3x+78=x | | a^8/a^24 | | 7x+10=x | | (8x10^13)(7.5x10^4)/(3.9x10^11)(2x10^3) | | 81p^2-(9p)-2=0 | | 1.2x-2.6=0.5x+1.18 | | 81p^2-9p-2=0 | | 36+58= | | x^2+2x-88=0 | | 3600n=180n-360 | | X+3y+6z=20 | | 3600=n-2*180 | | 135n=180n-360 | | 1.1x+4.2=0.7x+1.28 | | X+3y+6y=20 | | 12151515415415154154145788+1516516161561841= | | 12151515415415154154145788+15165161615618411= | | -6x^2+37x-22=0 | | 2(3+1)=6 | | 4a^2+20af+25f^2=0 | | 2(3x+1)=6 | | -0.1(50)+0.7x=0.3(50+x) | | 5cosx=3 | | 30+.10x+5x+.05x=x | | (1/3x*12)+(4*3)=4*6 | | 25r^2-80r+64=0 | | 4c^3+8c^2-96=0 | | 10n^2-13np-3p^2=0 | | 40*2x=30(2x+6) |

Equations solver categories