0=-0.125x^2+0.35x+0.75

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Solution for 0=-0.125x^2+0.35x+0.75 equation:


Simplifying
0 = -0.125x2 + 0.35x + 0.75

Reorder the terms:
0 = 0.75 + 0.35x + -0.125x2

Solving
0 = 0.75 + 0.35x + -0.125x2

Solving for variable 'x'.

Combine like terms: 0 + -0.75 = -0.75
-0.75 + -0.35x + 0.125x2 = 0.75 + 0.35x + -0.125x2 + -0.75 + -0.35x + 0.125x2

Reorder the terms:
-0.75 + -0.35x + 0.125x2 = 0.75 + -0.75 + 0.35x + -0.35x + -0.125x2 + 0.125x2

Combine like terms: 0.75 + -0.75 = 0.00
-0.75 + -0.35x + 0.125x2 = 0.00 + 0.35x + -0.35x + -0.125x2 + 0.125x2
-0.75 + -0.35x + 0.125x2 = 0.35x + -0.35x + -0.125x2 + 0.125x2

Combine like terms: 0.35x + -0.35x = 0.00
-0.75 + -0.35x + 0.125x2 = 0.00 + -0.125x2 + 0.125x2
-0.75 + -0.35x + 0.125x2 = -0.125x2 + 0.125x2

Combine like terms: -0.125x2 + 0.125x2 = 0.000
-0.75 + -0.35x + 0.125x2 = 0.000

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

Divide each side by '0.125'.
-6 + -2.8x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2.8x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -2.8x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -2.8x + x2 = 0 + 6
-2.8x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-2.8x + x2 = 6

The x term is -2.8x.  Take half its coefficient (-1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
-2.8x + 1.96 + x2 = 6 + 1.96

Reorder the terms:
1.96 + -2.8x + x2 = 6 + 1.96

Combine like terms: 6 + 1.96 = 7.96
1.96 + -2.8x + x2 = 7.96

Factor a perfect square on the left side:
(x + -1.4)(x + -1.4) = 7.96

Calculate the square root of the right side: 2.821347196

Break this problem into two subproblems by setting 
(x + -1.4) equal to 2.821347196 and -2.821347196.

Subproblem 1

x + -1.4 = 2.821347196 Simplifying x + -1.4 = 2.821347196 Reorder the terms: -1.4 + x = 2.821347196 Solving -1.4 + x = 2.821347196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 2.821347196 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 2.821347196 + 1.4 x = 2.821347196 + 1.4 Combine like terms: 2.821347196 + 1.4 = 4.221347196 x = 4.221347196 Simplifying x = 4.221347196

Subproblem 2

x + -1.4 = -2.821347196 Simplifying x + -1.4 = -2.821347196 Reorder the terms: -1.4 + x = -2.821347196 Solving -1.4 + x = -2.821347196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -2.821347196 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -2.821347196 + 1.4 x = -2.821347196 + 1.4 Combine like terms: -2.821347196 + 1.4 = -1.421347196 x = -1.421347196 Simplifying x = -1.421347196

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.221347196, -1.421347196}

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