7x(3x-5)=-11

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Solution for 7x(3x-5)=-11 equation:


Simplifying
7x(3x + -5) = -11

Reorder the terms:
7x(-5 + 3x) = -11
(-5 * 7x + 3x * 7x) = -11
(-35x + 21x2) = -11

Solving
-35x + 21x2 = -11

Solving for variable 'x'.

Reorder the terms:
11 + -35x + 21x2 = -11 + 11

Combine like terms: -11 + 11 = 0
11 + -35x + 21x2 = 0

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

Divide each side by '21'.
0.5238095238 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.5238095238' to each side of the equation.
0.5238095238 + -1.666666667x + -0.5238095238 + x2 = 0 + -0.5238095238

Reorder the terms:
0.5238095238 + -0.5238095238 + -1.666666667x + x2 = 0 + -0.5238095238

Combine like terms: 0.5238095238 + -0.5238095238 = 0.0000000000
0.0000000000 + -1.666666667x + x2 = 0 + -0.5238095238
-1.666666667x + x2 = 0 + -0.5238095238

Combine like terms: 0 + -0.5238095238 = -0.5238095238
-1.666666667x + x2 = -0.5238095238

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = -0.5238095238 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = -0.5238095238 + 0.6944444447

Combine like terms: -0.5238095238 + 0.6944444447 = 0.1706349209
0.6944444447 + -1.666666667x + x2 = 0.1706349209

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 0.1706349209

Calculate the square root of the right side: 0.4130798

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 0.4130798 and -0.4130798.

Subproblem 1

x + -0.8333333335 = 0.4130798 Simplifying x + -0.8333333335 = 0.4130798 Reorder the terms: -0.8333333335 + x = 0.4130798 Solving -0.8333333335 + x = 0.4130798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 0.4130798 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 0.4130798 + 0.8333333335 x = 0.4130798 + 0.8333333335 Combine like terms: 0.4130798 + 0.8333333335 = 1.2464131335 x = 1.2464131335 Simplifying x = 1.2464131335

Subproblem 2

x + -0.8333333335 = -0.4130798 Simplifying x + -0.8333333335 = -0.4130798 Reorder the terms: -0.8333333335 + x = -0.4130798 Solving -0.8333333335 + x = -0.4130798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -0.4130798 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -0.4130798 + 0.8333333335 x = -0.4130798 + 0.8333333335 Combine like terms: -0.4130798 + 0.8333333335 = 0.4202535335 x = 0.4202535335 Simplifying x = 0.4202535335

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.2464131335, 0.4202535335}

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