0=-.018x^2+.25x+.7

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Solution for 0=-.018x^2+.25x+.7 equation:


Simplifying
0 = -0.018x2 + 0.25x + 0.7

Reorder the terms:
0 = 0.7 + 0.25x + -0.018x2

Solving
0 = 0.7 + 0.25x + -0.018x2

Solving for variable 'x'.

Combine like terms: 0 + -0.7 = -0.7
-0.7 + -0.25x + 0.018x2 = 0.7 + 0.25x + -0.018x2 + -0.7 + -0.25x + 0.018x2

Reorder the terms:
-0.7 + -0.25x + 0.018x2 = 0.7 + -0.7 + 0.25x + -0.25x + -0.018x2 + 0.018x2

Combine like terms: 0.7 + -0.7 = 0.0
-0.7 + -0.25x + 0.018x2 = 0.0 + 0.25x + -0.25x + -0.018x2 + 0.018x2
-0.7 + -0.25x + 0.018x2 = 0.25x + -0.25x + -0.018x2 + 0.018x2

Combine like terms: 0.25x + -0.25x = 0.00
-0.7 + -0.25x + 0.018x2 = 0.00 + -0.018x2 + 0.018x2
-0.7 + -0.25x + 0.018x2 = -0.018x2 + 0.018x2

Combine like terms: -0.018x2 + 0.018x2 = 0.000
-0.7 + -0.25x + 0.018x2 = 0.000

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

Divide each side by '0.018'.
-38.88888889 + -13.88888889x + x2 = 0

Move the constant term to the right:

Add '38.88888889' to each side of the equation.
-38.88888889 + -13.88888889x + 38.88888889 + x2 = 0 + 38.88888889

Reorder the terms:
-38.88888889 + 38.88888889 + -13.88888889x + x2 = 0 + 38.88888889

Combine like terms: -38.88888889 + 38.88888889 = 0.00000000
0.00000000 + -13.88888889x + x2 = 0 + 38.88888889
-13.88888889x + x2 = 0 + 38.88888889

Combine like terms: 0 + 38.88888889 = 38.88888889
-13.88888889x + x2 = 38.88888889

The x term is -13.88888889x.  Take half its coefficient (-6.944444445).
Square it (48.22530865) and add it to both sides.

Add '48.22530865' to each side of the equation.
-13.88888889x + 48.22530865 + x2 = 38.88888889 + 48.22530865

Reorder the terms:
48.22530865 + -13.88888889x + x2 = 38.88888889 + 48.22530865

Combine like terms: 38.88888889 + 48.22530865 = 87.11419754
48.22530865 + -13.88888889x + x2 = 87.11419754

Factor a perfect square on the left side:
(x + -6.944444445)(x + -6.944444445) = 87.11419754

Calculate the square root of the right side: 9.333498676

Break this problem into two subproblems by setting 
(x + -6.944444445) equal to 9.333498676 and -9.333498676.

Subproblem 1

x + -6.944444445 = 9.333498676 Simplifying x + -6.944444445 = 9.333498676 Reorder the terms: -6.944444445 + x = 9.333498676 Solving -6.944444445 + x = 9.333498676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.944444445' to each side of the equation. -6.944444445 + 6.944444445 + x = 9.333498676 + 6.944444445 Combine like terms: -6.944444445 + 6.944444445 = 0.000000000 0.000000000 + x = 9.333498676 + 6.944444445 x = 9.333498676 + 6.944444445 Combine like terms: 9.333498676 + 6.944444445 = 16.277943121 x = 16.277943121 Simplifying x = 16.277943121

Subproblem 2

x + -6.944444445 = -9.333498676 Simplifying x + -6.944444445 = -9.333498676 Reorder the terms: -6.944444445 + x = -9.333498676 Solving -6.944444445 + x = -9.333498676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.944444445' to each side of the equation. -6.944444445 + 6.944444445 + x = -9.333498676 + 6.944444445 Combine like terms: -6.944444445 + 6.944444445 = 0.000000000 0.000000000 + x = -9.333498676 + 6.944444445 x = -9.333498676 + 6.944444445 Combine like terms: -9.333498676 + 6.944444445 = -2.389054231 x = -2.389054231 Simplifying x = -2.389054231

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.277943121, -2.389054231}

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