40=10x+0.7x^2

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Solution for 40=10x+0.7x^2 equation:


Simplifying
40 = 10x + 0.7x2

Solving
40 = 10x + 0.7x2

Solving for variable 'x'.

Reorder the terms:
40 + -10x + -0.7x2 = 10x + -10x + 0.7x2 + -0.7x2

Combine like terms: 10x + -10x = 0
40 + -10x + -0.7x2 = 0 + 0.7x2 + -0.7x2
40 + -10x + -0.7x2 = 0.7x2 + -0.7x2

Combine like terms: 0.7x2 + -0.7x2 = 0.0
40 + -10x + -0.7x2 = 0.0

Begin completing the square.  Divide all terms by
-0.7 the coefficient of the squared term: 

Divide each side by '-0.7'.
-57.14285714 + 14.28571429x + x2 = 0

Move the constant term to the right:

Add '57.14285714' to each side of the equation.
-57.14285714 + 14.28571429x + 57.14285714 + x2 = 0 + 57.14285714

Reorder the terms:
-57.14285714 + 57.14285714 + 14.28571429x + x2 = 0 + 57.14285714

Combine like terms: -57.14285714 + 57.14285714 = 0.00000000
0.00000000 + 14.28571429x + x2 = 0 + 57.14285714
14.28571429x + x2 = 0 + 57.14285714

Combine like terms: 0 + 57.14285714 = 57.14285714
14.28571429x + x2 = 57.14285714

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 = 57.14285714 + 51.02040819

Reorder the terms:
51.02040819 + 14.28571429x + x2 = 57.14285714 + 51.02040819

Combine like terms: 57.14285714 + 51.02040819 = 108.16326533
51.02040819 + 14.28571429x + x2 = 108.16326533

Factor a perfect square on the left side:
(x + 7.142857145)(x + 7.142857145) = 108.16326533

Calculate the square root of the right side: 10.400156986

Break this problem into two subproblems by setting 
(x + 7.142857145) equal to 10.400156986 and -10.400156986.

Subproblem 1

x + 7.142857145 = 10.400156986 Simplifying x + 7.142857145 = 10.400156986 Reorder the terms: 7.142857145 + x = 10.400156986 Solving 7.142857145 + x = 10.400156986 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 = 10.400156986 + -7.142857145 Combine like terms: 7.142857145 + -7.142857145 = 0.000000000 0.000000000 + x = 10.400156986 + -7.142857145 x = 10.400156986 + -7.142857145 Combine like terms: 10.400156986 + -7.142857145 = 3.257299841 x = 3.257299841 Simplifying x = 3.257299841

Subproblem 2

x + 7.142857145 = -10.400156986 Simplifying x + 7.142857145 = -10.400156986 Reorder the terms: 7.142857145 + x = -10.400156986 Solving 7.142857145 + x = -10.400156986 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 = -10.400156986 + -7.142857145 Combine like terms: 7.142857145 + -7.142857145 = 0.000000000 0.000000000 + x = -10.400156986 + -7.142857145 x = -10.400156986 + -7.142857145 Combine like terms: -10.400156986 + -7.142857145 = -17.543014131 x = -17.543014131 Simplifying x = -17.543014131

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.257299841, -17.543014131}

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