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Simplifying 45x2 + 60x = 20 Reorder the terms: 60x + 45x2 = 20 Solving 60x + 45x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 60x + 45x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 60x + 45x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-4 + 12x + 9x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-4 + 12x + 9x2)' equal to zero and attempt to solve: Simplifying -4 + 12x + 9x2 = 0 Solving -4 + 12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + 1.333333333x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + 1.333333333x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + 1.333333333x + x2 = 0 + 0.4444444444 1.333333333x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 1.333333333x + x2 = 0.4444444444 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 = 0.4444444444 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 0.4444444444 + 0.4444444442 Combine like terms: 0.4444444444 + 0.4444444442 = 0.8888888886 0.4444444442 + 1.333333333x + x2 = 0.8888888886 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 0.8888888886 Calculate the square root of the right side: 0.942809041 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 0.942809041 and -0.942809041.Subproblem 1
x + 0.6666666665 = 0.942809041 Simplifying x + 0.6666666665 = 0.942809041 Reorder the terms: 0.6666666665 + x = 0.942809041 Solving 0.6666666665 + x = 0.942809041 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 = 0.942809041 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 0.942809041 + -0.6666666665 x = 0.942809041 + -0.6666666665 Combine like terms: 0.942809041 + -0.6666666665 = 0.2761423745 x = 0.2761423745 Simplifying x = 0.2761423745Subproblem 2
x + 0.6666666665 = -0.942809041 Simplifying x + 0.6666666665 = -0.942809041 Reorder the terms: 0.6666666665 + x = -0.942809041 Solving 0.6666666665 + x = -0.942809041 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 = -0.942809041 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -0.942809041 + -0.6666666665 x = -0.942809041 + -0.6666666665 Combine like terms: -0.942809041 + -0.6666666665 = -1.6094757075 x = -1.6094757075 Simplifying x = -1.6094757075Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2761423745, -1.6094757075}Solution
x = {0.2761423745, -1.6094757075}
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