3.5=10x-5x^2

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Solution for 3.5=10x-5x^2 equation:


Simplifying
3.5 = 10x + -5x2

Solving
3.5 = 10x + -5x2

Solving for variable 'x'.

Reorder the terms:
3.5 + -10x + 5x2 = 10x + -10x + -5x2 + 5x2

Combine like terms: 10x + -10x = 0
3.5 + -10x + 5x2 = 0 + -5x2 + 5x2
3.5 + -10x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
3.5 + -10x + 5x2 = 0

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

Divide each side by '5'.
0.7 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.7' to each side of the equation.
0.7 + -2x + -0.7 + x2 = 0 + -0.7

Reorder the terms:
0.7 + -0.7 + -2x + x2 = 0 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + -2x + x2 = 0 + -0.7
-2x + x2 = 0 + -0.7

Combine like terms: 0 + -0.7 = -0.7
-2x + x2 = -0.7

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.7 + 1

Reorder the terms:
1 + -2x + x2 = -0.7 + 1

Combine like terms: -0.7 + 1 = 0.3
1 + -2x + x2 = 0.3

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.3

Calculate the square root of the right side: 0.547722558

Break this problem into two subproblems by setting 
(x + -1) equal to 0.547722558 and -0.547722558.

Subproblem 1

x + -1 = 0.547722558 Simplifying x + -1 = 0.547722558 Reorder the terms: -1 + x = 0.547722558 Solving -1 + x = 0.547722558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.547722558 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.547722558 + 1 x = 0.547722558 + 1 Combine like terms: 0.547722558 + 1 = 1.547722558 x = 1.547722558 Simplifying x = 1.547722558

Subproblem 2

x + -1 = -0.547722558 Simplifying x + -1 = -0.547722558 Reorder the terms: -1 + x = -0.547722558 Solving -1 + x = -0.547722558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.547722558 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.547722558 + 1 x = -0.547722558 + 1 Combine like terms: -0.547722558 + 1 = 0.452277442 x = 0.452277442 Simplifying x = 0.452277442

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.547722558, 0.452277442}

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