x(2x+5)=140

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Solution for x(2x+5)=140 equation:


Simplifying
x(2x + 5) = 140

Reorder the terms:
x(5 + 2x) = 140
(5 * x + 2x * x) = 140
(5x + 2x2) = 140

Solving
5x + 2x2 = 140

Solving for variable 'x'.

Reorder the terms:
-140 + 5x + 2x2 = 140 + -140

Combine like terms: 140 + -140 = 0
-140 + 5x + 2x2 = 0

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

Divide each side by '2'.
-70 + 2.5x + x2 = 0

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + 2.5x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + 2.5x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 2.5x + x2 = 0 + 70
2.5x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
2.5x + x2 = 70

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 70 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 70 + 1.5625

Combine like terms: 70 + 1.5625 = 71.5625
1.5625 + 2.5x + x2 = 71.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 71.5625

Calculate the square root of the right side: 8.459462158

Break this problem into two subproblems by setting 
(x + 1.25) equal to 8.459462158 and -8.459462158.

Subproblem 1

x + 1.25 = 8.459462158 Simplifying x + 1.25 = 8.459462158 Reorder the terms: 1.25 + x = 8.459462158 Solving 1.25 + x = 8.459462158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 8.459462158 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 8.459462158 + -1.25 x = 8.459462158 + -1.25 Combine like terms: 8.459462158 + -1.25 = 7.209462158 x = 7.209462158 Simplifying x = 7.209462158

Subproblem 2

x + 1.25 = -8.459462158 Simplifying x + 1.25 = -8.459462158 Reorder the terms: 1.25 + x = -8.459462158 Solving 1.25 + x = -8.459462158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -8.459462158 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -8.459462158 + -1.25 x = -8.459462158 + -1.25 Combine like terms: -8.459462158 + -1.25 = -9.709462158 x = -9.709462158 Simplifying x = -9.709462158

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.209462158, -9.709462158}

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