0=-16x^2+58x+3

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Solution for 0=-16x^2+58x+3 equation:


Simplifying
0 = -16x2 + 58x + 3

Reorder the terms:
0 = 3 + 58x + -16x2

Solving
0 = 3 + 58x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + -3 = -3
-3 + -58x + 16x2 = 3 + 58x + -16x2 + -3 + -58x + 16x2

Reorder the terms:
-3 + -58x + 16x2 = 3 + -3 + 58x + -58x + -16x2 + 16x2

Combine like terms: 3 + -3 = 0
-3 + -58x + 16x2 = 0 + 58x + -58x + -16x2 + 16x2
-3 + -58x + 16x2 = 58x + -58x + -16x2 + 16x2

Combine like terms: 58x + -58x = 0
-3 + -58x + 16x2 = 0 + -16x2 + 16x2
-3 + -58x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-3 + -58x + 16x2 = 0

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

Divide each side by '16'.
-0.1875 + -3.625x + x2 = 0

Move the constant term to the right:

Add '0.1875' to each side of the equation.
-0.1875 + -3.625x + 0.1875 + x2 = 0 + 0.1875

Reorder the terms:
-0.1875 + 0.1875 + -3.625x + x2 = 0 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + -3.625x + x2 = 0 + 0.1875
-3.625x + x2 = 0 + 0.1875

Combine like terms: 0 + 0.1875 = 0.1875
-3.625x + x2 = 0.1875

The x term is -3.625x.  Take half its coefficient (-1.8125).
Square it (3.28515625) and add it to both sides.

Add '3.28515625' to each side of the equation.
-3.625x + 3.28515625 + x2 = 0.1875 + 3.28515625

Reorder the terms:
3.28515625 + -3.625x + x2 = 0.1875 + 3.28515625

Combine like terms: 0.1875 + 3.28515625 = 3.47265625
3.28515625 + -3.625x + x2 = 3.47265625

Factor a perfect square on the left side:
(x + -1.8125)(x + -1.8125) = 3.47265625

Calculate the square root of the right side: 1.863506439

Break this problem into two subproblems by setting 
(x + -1.8125) equal to 1.863506439 and -1.863506439.

Subproblem 1

x + -1.8125 = 1.863506439 Simplifying x + -1.8125 = 1.863506439 Reorder the terms: -1.8125 + x = 1.863506439 Solving -1.8125 + x = 1.863506439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8125' to each side of the equation. -1.8125 + 1.8125 + x = 1.863506439 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + x = 1.863506439 + 1.8125 x = 1.863506439 + 1.8125 Combine like terms: 1.863506439 + 1.8125 = 3.676006439 x = 3.676006439 Simplifying x = 3.676006439

Subproblem 2

x + -1.8125 = -1.863506439 Simplifying x + -1.8125 = -1.863506439 Reorder the terms: -1.8125 + x = -1.863506439 Solving -1.8125 + x = -1.863506439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8125' to each side of the equation. -1.8125 + 1.8125 + x = -1.863506439 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + x = -1.863506439 + 1.8125 x = -1.863506439 + 1.8125 Combine like terms: -1.863506439 + 1.8125 = -0.051006439 x = -0.051006439 Simplifying x = -0.051006439

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.676006439, -0.051006439}

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