7x^2+64x=100

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Solution for 7x^2+64x=100 equation:


Simplifying
7x2 + 64x = 100

Reorder the terms:
64x + 7x2 = 100

Solving
64x + 7x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + 64x + 7x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 64x + 7x2 = 0

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

Divide each side by '7'.
-14.28571429 + 9.142857143x + x2 = 0

Move the constant term to the right:

Add '14.28571429' to each side of the equation.
-14.28571429 + 9.142857143x + 14.28571429 + x2 = 0 + 14.28571429

Reorder the terms:
-14.28571429 + 14.28571429 + 9.142857143x + x2 = 0 + 14.28571429

Combine like terms: -14.28571429 + 14.28571429 = 0.00000000
0.00000000 + 9.142857143x + x2 = 0 + 14.28571429
9.142857143x + x2 = 0 + 14.28571429

Combine like terms: 0 + 14.28571429 = 14.28571429
9.142857143x + x2 = 14.28571429

The x term is 9.142857143x.  Take half its coefficient (4.571428572).
Square it (20.89795919) and add it to both sides.

Add '20.89795919' to each side of the equation.
9.142857143x + 20.89795919 + x2 = 14.28571429 + 20.89795919

Reorder the terms:
20.89795919 + 9.142857143x + x2 = 14.28571429 + 20.89795919

Combine like terms: 14.28571429 + 20.89795919 = 35.18367348
20.89795919 + 9.142857143x + x2 = 35.18367348

Factor a perfect square on the left side:
(x + 4.571428572)(x + 4.571428572) = 35.18367348

Calculate the square root of the right side: 5.931582713

Break this problem into two subproblems by setting 
(x + 4.571428572) equal to 5.931582713 and -5.931582713.

Subproblem 1

x + 4.571428572 = 5.931582713 Simplifying x + 4.571428572 = 5.931582713 Reorder the terms: 4.571428572 + x = 5.931582713 Solving 4.571428572 + x = 5.931582713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.571428572' to each side of the equation. 4.571428572 + -4.571428572 + x = 5.931582713 + -4.571428572 Combine like terms: 4.571428572 + -4.571428572 = 0.000000000 0.000000000 + x = 5.931582713 + -4.571428572 x = 5.931582713 + -4.571428572 Combine like terms: 5.931582713 + -4.571428572 = 1.360154141 x = 1.360154141 Simplifying x = 1.360154141

Subproblem 2

x + 4.571428572 = -5.931582713 Simplifying x + 4.571428572 = -5.931582713 Reorder the terms: 4.571428572 + x = -5.931582713 Solving 4.571428572 + x = -5.931582713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.571428572' to each side of the equation. 4.571428572 + -4.571428572 + x = -5.931582713 + -4.571428572 Combine like terms: 4.571428572 + -4.571428572 = 0.000000000 0.000000000 + x = -5.931582713 + -4.571428572 x = -5.931582713 + -4.571428572 Combine like terms: -5.931582713 + -4.571428572 = -10.503011285 x = -10.503011285 Simplifying x = -10.503011285

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.360154141, -10.503011285}

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