7x^2+100x-24=0

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Solution for 7x^2+100x-24=0 equation:


Simplifying
7x2 + 100x + -24 = 0

Reorder the terms:
-24 + 100x + 7x2 = 0

Solving
-24 + 100x + 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'.
-3.428571429 + 14.28571429x + x2 = 0

Move the constant term to the right:

Add '3.428571429' to each side of the equation.
-3.428571429 + 14.28571429x + 3.428571429 + x2 = 0 + 3.428571429

Reorder the terms:
-3.428571429 + 3.428571429 + 14.28571429x + x2 = 0 + 3.428571429

Combine like terms: -3.428571429 + 3.428571429 = 0.000000000
0.000000000 + 14.28571429x + x2 = 0 + 3.428571429
14.28571429x + x2 = 0 + 3.428571429

Combine like terms: 0 + 3.428571429 = 3.428571429
14.28571429x + x2 = 3.428571429

The x term is 14.28571429x.  Take half its coefficient (7.142857145).
Square it (51.02040819) and add it to both sides.

Add '51.02040819' to each side of the equation.
14.28571429x + 51.02040819 + x2 = 3.428571429 + 51.02040819

Reorder the terms:
51.02040819 + 14.28571429x + x2 = 3.428571429 + 51.02040819

Combine like terms: 3.428571429 + 51.02040819 = 54.448979619
51.02040819 + 14.28571429x + x2 = 54.448979619

Factor a perfect square on the left side:
(x + 7.142857145)(x + 7.142857145) = 54.448979619

Calculate the square root of the right side: 7.378955185

Break this problem into two subproblems by setting 
(x + 7.142857145) equal to 7.378955185 and -7.378955185.

Subproblem 1

x + 7.142857145 = 7.378955185 Simplifying x + 7.142857145 = 7.378955185 Reorder the terms: 7.142857145 + x = 7.378955185 Solving 7.142857145 + x = 7.378955185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.142857145' to each side of the equation. 7.142857145 + -7.142857145 + x = 7.378955185 + -7.142857145 Combine like terms: 7.142857145 + -7.142857145 = 0.000000000 0.000000000 + x = 7.378955185 + -7.142857145 x = 7.378955185 + -7.142857145 Combine like terms: 7.378955185 + -7.142857145 = 0.23609804 x = 0.23609804 Simplifying x = 0.23609804

Subproblem 2

x + 7.142857145 = -7.378955185 Simplifying x + 7.142857145 = -7.378955185 Reorder the terms: 7.142857145 + x = -7.378955185 Solving 7.142857145 + x = -7.378955185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.142857145' to each side of the equation. 7.142857145 + -7.142857145 + x = -7.378955185 + -7.142857145 Combine like terms: 7.142857145 + -7.142857145 = 0.000000000 0.000000000 + x = -7.378955185 + -7.142857145 x = -7.378955185 + -7.142857145 Combine like terms: -7.378955185 + -7.142857145 = -14.52181233 x = -14.52181233 Simplifying x = -14.52181233

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.23609804, -14.52181233}

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