-100a^2+35a-2.25=0

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Solution for -100a^2+35a-2.25=0 equation:


Simplifying
-100a2 + 35a + -2.25 = 0

Reorder the terms:
-2.25 + 35a + -100a2 = 0

Solving
-2.25 + 35a + -100a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
-100 the coefficient of the squared term: 

Divide each side by '-100'.
0.0225 + -0.35a + a2 = 0

Move the constant term to the right:

Add '-0.0225' to each side of the equation.
0.0225 + -0.35a + -0.0225 + a2 = 0 + -0.0225

Reorder the terms:
0.0225 + -0.0225 + -0.35a + a2 = 0 + -0.0225

Combine like terms: 0.0225 + -0.0225 = 0.0000
0.0000 + -0.35a + a2 = 0 + -0.0225
-0.35a + a2 = 0 + -0.0225

Combine like terms: 0 + -0.0225 = -0.0225
-0.35a + a2 = -0.0225

The a term is -0.35a.  Take half its coefficient (-0.175).
Square it (0.030625) and add it to both sides.

Add '0.030625' to each side of the equation.
-0.35a + 0.030625 + a2 = -0.0225 + 0.030625

Reorder the terms:
0.030625 + -0.35a + a2 = -0.0225 + 0.030625

Combine like terms: -0.0225 + 0.030625 = 0.008125
0.030625 + -0.35a + a2 = 0.008125

Factor a perfect square on the left side:
(a + -0.175)(a + -0.175) = 0.008125

Calculate the square root of the right side: 0.090138782

Break this problem into two subproblems by setting 
(a + -0.175) equal to 0.090138782 and -0.090138782.

Subproblem 1

a + -0.175 = 0.090138782 Simplifying a + -0.175 = 0.090138782 Reorder the terms: -0.175 + a = 0.090138782 Solving -0.175 + a = 0.090138782 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.175' to each side of the equation. -0.175 + 0.175 + a = 0.090138782 + 0.175 Combine like terms: -0.175 + 0.175 = 0.000 0.000 + a = 0.090138782 + 0.175 a = 0.090138782 + 0.175 Combine like terms: 0.090138782 + 0.175 = 0.265138782 a = 0.265138782 Simplifying a = 0.265138782

Subproblem 2

a + -0.175 = -0.090138782 Simplifying a + -0.175 = -0.090138782 Reorder the terms: -0.175 + a = -0.090138782 Solving -0.175 + a = -0.090138782 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.175' to each side of the equation. -0.175 + 0.175 + a = -0.090138782 + 0.175 Combine like terms: -0.175 + 0.175 = 0.000 0.000 + a = -0.090138782 + 0.175 a = -0.090138782 + 0.175 Combine like terms: -0.090138782 + 0.175 = 0.084861218 a = 0.084861218 Simplifying a = 0.084861218

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.265138782, 0.084861218}

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