7x^2+5x-14=0

Simple and best practice solution for 7x^2+5x-14=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 7x^2+5x-14=0 equation:


Simplifying
7x2 + 5x + -14 = 0

Reorder the terms:
-14 + 5x + 7x2 = 0

Solving
-14 + 5x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-2 + 0.7142857143x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 0.7142857143x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 0.7142857143x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 0.7142857143x + x2 = 0 + 2
0.7142857143x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
0.7142857143x + x2 = 2

The x term is 0.7142857143x.  Take half its coefficient (0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
0.7142857143x + 0.1275510204 + x2 = 2 + 0.1275510204

Reorder the terms:
0.1275510204 + 0.7142857143x + x2 = 2 + 0.1275510204

Combine like terms: 2 + 0.1275510204 = 2.1275510204
0.1275510204 + 0.7142857143x + x2 = 2.1275510204

Factor a perfect square on the left side:
(x + 0.3571428572)(x + 0.3571428572) = 2.1275510204

Calculate the square root of the right side: 1.458612704

Break this problem into two subproblems by setting 
(x + 0.3571428572) equal to 1.458612704 and -1.458612704.

Subproblem 1

x + 0.3571428572 = 1.458612704 Simplifying x + 0.3571428572 = 1.458612704 Reorder the terms: 0.3571428572 + x = 1.458612704 Solving 0.3571428572 + x = 1.458612704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = 1.458612704 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 1.458612704 + -0.3571428572 x = 1.458612704 + -0.3571428572 Combine like terms: 1.458612704 + -0.3571428572 = 1.1014698468 x = 1.1014698468 Simplifying x = 1.1014698468

Subproblem 2

x + 0.3571428572 = -1.458612704 Simplifying x + 0.3571428572 = -1.458612704 Reorder the terms: 0.3571428572 + x = -1.458612704 Solving 0.3571428572 + x = -1.458612704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = -1.458612704 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -1.458612704 + -0.3571428572 x = -1.458612704 + -0.3571428572 Combine like terms: -1.458612704 + -0.3571428572 = -1.8157555612 x = -1.8157555612 Simplifying x = -1.8157555612

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.1014698468, -1.8157555612}

See similar equations:

| 5=[2A-5B+C] | | 2x+10=125 | | 2x-10=125 | | 15h^2-7h-2= | | -36+4x=-24 | | 40=40-10t-5t^2 | | 19-x/4=14 | | 8x^2-33x-35=0 | | 1/2-4/3w=-4/5 | | A-B=2+C | | 10x^2-31x-36=0 | | (X+y)(9x^2-2xy+8y^2)= | | =x-3y(x-8y)-(-6xy+7x) | | (x-8)(x+12)=0 | | 5n^2-6n+5=0 | | 2g-8=10 | | -1=x^2 | | 6m+16=4 | | 87/10-63/10 | | 4+xi+2yi=x+2i | | 4=x/7.8 | | 10x+y=8628 | | (h-3/5)(h-3/5)=1/2 | | (x-3)=3x+9 | | 19-18= | | -36+4x=-8 | | 3x+x=98 | | 49=x(x+4) | | 155+2t+4=5+6t+8 | | 4+19x-3=9x+91-5x | | -4(x-3)=-2(x+y+5) | | -6(x-4)=-3(x-5) |

Equations solver categories