45x^2=6-60x

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Solution for 45x^2=6-60x equation:


Simplifying
45x2 = 6 + -60x

Solving
45x2 = 6 + -60x

Solving for variable 'x'.

Reorder the terms:
-6 + 60x + 45x2 = 6 + -60x + -6 + 60x

Reorder the terms:
-6 + 60x + 45x2 = 6 + -6 + -60x + 60x

Combine like terms: 6 + -6 = 0
-6 + 60x + 45x2 = 0 + -60x + 60x
-6 + 60x + 45x2 = -60x + 60x

Combine like terms: -60x + 60x = 0
-6 + 60x + 45x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 20x + 15x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-2 + 20x + 15x2)' equal to zero and attempt to solve: Simplifying -2 + 20x + 15x2 = 0 Solving -2 + 20x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.1333333333 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '0.1333333333' to each side of the equation. -0.1333333333 + 1.333333333x + 0.1333333333 + x2 = 0 + 0.1333333333 Reorder the terms: -0.1333333333 + 0.1333333333 + 1.333333333x + x2 = 0 + 0.1333333333 Combine like terms: -0.1333333333 + 0.1333333333 = 0.0000000000 0.0000000000 + 1.333333333x + x2 = 0 + 0.1333333333 1.333333333x + x2 = 0 + 0.1333333333 Combine like terms: 0 + 0.1333333333 = 0.1333333333 1.333333333x + x2 = 0.1333333333 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 0.1333333333 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 0.1333333333 + 0.4444444442 Combine like terms: 0.1333333333 + 0.4444444442 = 0.5777777775 0.4444444442 + 1.333333333x + x2 = 0.5777777775 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 0.5777777775 Calculate the square root of the right side: 0.76011695 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 0.76011695 and -0.76011695.

Subproblem 1

x + 0.6666666665 = 0.76011695 Simplifying x + 0.6666666665 = 0.76011695 Reorder the terms: 0.6666666665 + x = 0.76011695 Solving 0.6666666665 + x = 0.76011695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 0.76011695 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 0.76011695 + -0.6666666665 x = 0.76011695 + -0.6666666665 Combine like terms: 0.76011695 + -0.6666666665 = 0.0934502835 x = 0.0934502835 Simplifying x = 0.0934502835

Subproblem 2

x + 0.6666666665 = -0.76011695 Simplifying x + 0.6666666665 = -0.76011695 Reorder the terms: 0.6666666665 + x = -0.76011695 Solving 0.6666666665 + x = -0.76011695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -0.76011695 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -0.76011695 + -0.6666666665 x = -0.76011695 + -0.6666666665 Combine like terms: -0.76011695 + -0.6666666665 = -1.4267836165 x = -1.4267836165 Simplifying x = -1.4267836165

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.0934502835, -1.4267836165}

Solution

x = {0.0934502835, -1.4267836165}

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