0=-10x^2+36x+184

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Solution for 0=-10x^2+36x+184 equation:


Simplifying
0 = -10x2 + 36x + 184

Reorder the terms:
0 = 184 + 36x + -10x2

Solving
0 = 184 + 36x + -10x2

Solving for variable 'x'.

Combine like terms: 0 + -184 = -184
-184 + -36x + 10x2 = 184 + 36x + -10x2 + -184 + -36x + 10x2

Reorder the terms:
-184 + -36x + 10x2 = 184 + -184 + 36x + -36x + -10x2 + 10x2

Combine like terms: 184 + -184 = 0
-184 + -36x + 10x2 = 0 + 36x + -36x + -10x2 + 10x2
-184 + -36x + 10x2 = 36x + -36x + -10x2 + 10x2

Combine like terms: 36x + -36x = 0
-184 + -36x + 10x2 = 0 + -10x2 + 10x2
-184 + -36x + 10x2 = -10x2 + 10x2

Combine like terms: -10x2 + 10x2 = 0
-184 + -36x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-92 + -18x + 5x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-92 + -18x + 5x2)' equal to zero and attempt to solve: Simplifying -92 + -18x + 5x2 = 0 Solving -92 + -18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -18.4 + -3.6x + x2 = 0 Move the constant term to the right: Add '18.4' to each side of the equation. -18.4 + -3.6x + 18.4 + x2 = 0 + 18.4 Reorder the terms: -18.4 + 18.4 + -3.6x + x2 = 0 + 18.4 Combine like terms: -18.4 + 18.4 = 0.0 0.0 + -3.6x + x2 = 0 + 18.4 -3.6x + x2 = 0 + 18.4 Combine like terms: 0 + 18.4 = 18.4 -3.6x + x2 = 18.4 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = 18.4 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = 18.4 + 3.24 Combine like terms: 18.4 + 3.24 = 21.64 3.24 + -3.6x + x2 = 21.64 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 21.64 Calculate the square root of the right side: 4.65188134 Break this problem into two subproblems by setting (x + -1.8) equal to 4.65188134 and -4.65188134.

Subproblem 1

x + -1.8 = 4.65188134 Simplifying x + -1.8 = 4.65188134 Reorder the terms: -1.8 + x = 4.65188134 Solving -1.8 + x = 4.65188134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 4.65188134 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 4.65188134 + 1.8 x = 4.65188134 + 1.8 Combine like terms: 4.65188134 + 1.8 = 6.45188134 x = 6.45188134 Simplifying x = 6.45188134

Subproblem 2

x + -1.8 = -4.65188134 Simplifying x + -1.8 = -4.65188134 Reorder the terms: -1.8 + x = -4.65188134 Solving -1.8 + x = -4.65188134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -4.65188134 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -4.65188134 + 1.8 x = -4.65188134 + 1.8 Combine like terms: -4.65188134 + 1.8 = -2.85188134 x = -2.85188134 Simplifying x = -2.85188134

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.45188134, -2.85188134}

Solution

x = {6.45188134, -2.85188134}

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