0=-9x^2+9x+9

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Solution for 0=-9x^2+9x+9 equation:


Simplifying
0 = -9x2 + 9x + 9

Reorder the terms:
0 = 9 + 9x + -9x2

Solving
0 = 9 + 9x + -9x2

Solving for variable 'x'.

Combine like terms: 0 + -9 = -9
-9 + -9x + 9x2 = 9 + 9x + -9x2 + -9 + -9x + 9x2

Reorder the terms:
-9 + -9x + 9x2 = 9 + -9 + 9x + -9x + -9x2 + 9x2

Combine like terms: 9 + -9 = 0
-9 + -9x + 9x2 = 0 + 9x + -9x + -9x2 + 9x2
-9 + -9x + 9x2 = 9x + -9x + -9x2 + 9x2

Combine like terms: 9x + -9x = 0
-9 + -9x + 9x2 = 0 + -9x2 + 9x2
-9 + -9x + 9x2 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-9 + -9x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-1 + -1x + x2) = 0

Ignore the factor 9.

Subproblem 1

Set the factor '(-1 + -1x + x2)' equal to zero and attempt to solve: Simplifying -1 + -1x + x2 = 0 Solving -1 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -1x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x + x2 = 0 + 1 -1x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1x + x2 = 1 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 1 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1 + 0.25 Combine like terms: 1 + 0.25 = 1.25 0.25 + -1x + x2 = 1.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + -0.5 = 1.118033989 Simplifying x + -0.5 = 1.118033989 Reorder the terms: -0.5 + x = 1.118033989 Solving -0.5 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.118033989 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.118033989 + 0.5 x = 1.118033989 + 0.5 Combine like terms: 1.118033989 + 0.5 = 1.618033989 x = 1.618033989 Simplifying x = 1.618033989

Subproblem 2

x + -0.5 = -1.118033989 Simplifying x + -0.5 = -1.118033989 Reorder the terms: -0.5 + x = -1.118033989 Solving -0.5 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.118033989 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.118033989 + 0.5 x = -1.118033989 + 0.5 Combine like terms: -1.118033989 + 0.5 = -0.618033989 x = -0.618033989 Simplifying x = -0.618033989

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.618033989, -0.618033989}

Solution

x = {1.618033989, -0.618033989}

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