4x^2+14x-13=0

Simple and best practice solution for 4x^2+14x-13=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+14x-13=0 equation:


Simplifying
4x2 + 14x + -13 = 0

Reorder the terms:
-13 + 14x + 4x2 = 0

Solving
-13 + 14x + 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'.
-3.25 + 3.5x + x2 = 0

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + 3.5x + 3.25 + x2 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + 3.5x + x2 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + 3.5x + x2 = 0 + 3.25
3.5x + x2 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
3.5x + x2 = 3.25

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 3.25 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 3.25 + 3.0625

Combine like terms: 3.25 + 3.0625 = 6.3125
3.0625 + 3.5x + x2 = 6.3125

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 6.3125

Calculate the square root of the right side: 2.512468905

Break this problem into two subproblems by setting 
(x + 1.75) equal to 2.512468905 and -2.512468905.

Subproblem 1

x + 1.75 = 2.512468905 Simplifying x + 1.75 = 2.512468905 Reorder the terms: 1.75 + x = 2.512468905 Solving 1.75 + x = 2.512468905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 2.512468905 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 2.512468905 + -1.75 x = 2.512468905 + -1.75 Combine like terms: 2.512468905 + -1.75 = 0.762468905 x = 0.762468905 Simplifying x = 0.762468905

Subproblem 2

x + 1.75 = -2.512468905 Simplifying x + 1.75 = -2.512468905 Reorder the terms: 1.75 + x = -2.512468905 Solving 1.75 + x = -2.512468905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -2.512468905 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -2.512468905 + -1.75 x = -2.512468905 + -1.75 Combine like terms: -2.512468905 + -1.75 = -4.262468905 x = -4.262468905 Simplifying x = -4.262468905

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.762468905, -4.262468905}

See similar equations:

| .9(8x+9)=5.2-(x-3) | | s*5+40=115 | | log(4)*(5x+3)=2 | | 0.5(9x+6)=0.1-(x-3) | | x^2+(x^2+14x+7x+49)=x^2+(x^2+8x+8x+64) | | 4b-10=2b+8 | | 2m^2-5m-63=0 | | 3y+35=5+7y | | .14(y-4)+.10y=.04y-.05(30) | | 4x-(7+K)=-(6X+7) | | 2+2.50x=y | | 2-16t=6(3t+2) | | -3(4b+4)+(13b-7)=0 | | 2(150+-2Y)+4Y=300 | | -6.8x=47.6 | | (x+3i+1)(x-3i+1)=0 | | 11x-14x=27 | | -10x-5+10=75 | | 6x+3x=36 | | 2.9r=8.7 | | N+22=13 | | n+10.7=-23 | | 4x+3=35+(2x+16) | | 5(8t+1)-7=t-(t+1) | | 16x-64=100 | | -16+s=-48 | | 3(5m-2)=12 | | 4(7t+1)-12=t-(t+7) | | 8k-(9+K)=-(5K+9) | | 5Y-2Y+2=8 | | -4(4n-1)=24 | | 7z+3=2 |

Equations solver categories