3.75x^2-7x-120=0

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Solution for 3.75x^2-7x-120=0 equation:


Simplifying
3.75x2 + -7x + -120 = 0

Reorder the terms:
-120 + -7x + 3.75x2 = 0

Solving
-120 + -7x + 3.75x2 = 0

Solving for variable 'x'.

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

Divide each side by '3.75'.
-32 + -1.866666667x + x2 = 0

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -1.866666667x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + -1.866666667x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -1.866666667x + x2 = 0 + 32
-1.866666667x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
-1.866666667x + x2 = 32

The x term is -1.866666667x.  Take half its coefficient (-0.9333333335).
Square it (0.8711111114) and add it to both sides.

Add '0.8711111114' to each side of the equation.
-1.866666667x + 0.8711111114 + x2 = 32 + 0.8711111114

Reorder the terms:
0.8711111114 + -1.866666667x + x2 = 32 + 0.8711111114

Combine like terms: 32 + 0.8711111114 = 32.8711111114
0.8711111114 + -1.866666667x + x2 = 32.8711111114

Factor a perfect square on the left side:
(x + -0.9333333335)(x + -0.9333333335) = 32.8711111114

Calculate the square root of the right side: 5.733333333

Break this problem into two subproblems by setting 
(x + -0.9333333335) equal to 5.733333333 and -5.733333333.

Subproblem 1

x + -0.9333333335 = 5.733333333 Simplifying x + -0.9333333335 = 5.733333333 Reorder the terms: -0.9333333335 + x = 5.733333333 Solving -0.9333333335 + x = 5.733333333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9333333335' to each side of the equation. -0.9333333335 + 0.9333333335 + x = 5.733333333 + 0.9333333335 Combine like terms: -0.9333333335 + 0.9333333335 = 0.0000000000 0.0000000000 + x = 5.733333333 + 0.9333333335 x = 5.733333333 + 0.9333333335 Combine like terms: 5.733333333 + 0.9333333335 = 6.6666666665 x = 6.6666666665 Simplifying x = 6.6666666665

Subproblem 2

x + -0.9333333335 = -5.733333333 Simplifying x + -0.9333333335 = -5.733333333 Reorder the terms: -0.9333333335 + x = -5.733333333 Solving -0.9333333335 + x = -5.733333333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9333333335' to each side of the equation. -0.9333333335 + 0.9333333335 + x = -5.733333333 + 0.9333333335 Combine like terms: -0.9333333335 + 0.9333333335 = 0.0000000000 0.0000000000 + x = -5.733333333 + 0.9333333335 x = -5.733333333 + 0.9333333335 Combine like terms: -5.733333333 + 0.9333333335 = -4.7999999995 x = -4.7999999995 Simplifying x = -4.7999999995

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.6666666665, -4.7999999995}

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