x(2x+7)=250

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Solution for x(2x+7)=250 equation:


Simplifying
x(2x + 7) = 250

Reorder the terms:
x(7 + 2x) = 250
(7 * x + 2x * x) = 250
(7x + 2x2) = 250

Solving
7x + 2x2 = 250

Solving for variable 'x'.

Reorder the terms:
-250 + 7x + 2x2 = 250 + -250

Combine like terms: 250 + -250 = 0
-250 + 7x + 2x2 = 0

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

Divide each side by '2'.
-125 + 3.5x + x2 = 0

Move the constant term to the right:

Add '125' to each side of the equation.
-125 + 3.5x + 125 + x2 = 0 + 125

Reorder the terms:
-125 + 125 + 3.5x + x2 = 0 + 125

Combine like terms: -125 + 125 = 0
0 + 3.5x + x2 = 0 + 125
3.5x + x2 = 0 + 125

Combine like terms: 0 + 125 = 125
3.5x + x2 = 125

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 125 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 125 + 3.0625

Combine like terms: 125 + 3.0625 = 128.0625
3.0625 + 3.5x + x2 = 128.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 128.0625

Calculate the square root of the right side: 11.316470298

Break this problem into two subproblems by setting 
(x + 1.75) equal to 11.316470298 and -11.316470298.

Subproblem 1

x + 1.75 = 11.316470298 Simplifying x + 1.75 = 11.316470298 Reorder the terms: 1.75 + x = 11.316470298 Solving 1.75 + x = 11.316470298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 11.316470298 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 11.316470298 + -1.75 x = 11.316470298 + -1.75 Combine like terms: 11.316470298 + -1.75 = 9.566470298 x = 9.566470298 Simplifying x = 9.566470298

Subproblem 2

x + 1.75 = -11.316470298 Simplifying x + 1.75 = -11.316470298 Reorder the terms: 1.75 + x = -11.316470298 Solving 1.75 + x = -11.316470298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -11.316470298 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -11.316470298 + -1.75 x = -11.316470298 + -1.75 Combine like terms: -11.316470298 + -1.75 = -13.066470298 x = -13.066470298 Simplifying x = -13.066470298

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.566470298, -13.066470298}

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