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Simplifying 15x2 + 2x + -12 = 0 Reorder the terms: -12 + 2x + 15x2 = 0 Solving -12 + 2x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.8 + 0.1333333333x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 0.1333333333x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 0.1333333333x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 0.1333333333x + x2 = 0 + 0.8 0.1333333333x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 0.1333333333x + x2 = 0.8 The x term is 0.1333333333x. Take half its coefficient (0.06666666665). Square it (0.004444444442) and add it to both sides. Add '0.004444444442' to each side of the equation. 0.1333333333x + 0.004444444442 + x2 = 0.8 + 0.004444444442 Reorder the terms: 0.004444444442 + 0.1333333333x + x2 = 0.8 + 0.004444444442 Combine like terms: 0.8 + 0.004444444442 = 0.804444444442 0.004444444442 + 0.1333333333x + x2 = 0.804444444442 Factor a perfect square on the left side: (x + 0.06666666665)(x + 0.06666666665) = 0.804444444442 Calculate the square root of the right side: 0.89690827 Break this problem into two subproblems by setting (x + 0.06666666665) equal to 0.89690827 and -0.89690827.Subproblem 1
x + 0.06666666665 = 0.89690827 Simplifying x + 0.06666666665 = 0.89690827 Reorder the terms: 0.06666666665 + x = 0.89690827 Solving 0.06666666665 + x = 0.89690827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06666666665' to each side of the equation. 0.06666666665 + -0.06666666665 + x = 0.89690827 + -0.06666666665 Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000 0.00000000000 + x = 0.89690827 + -0.06666666665 x = 0.89690827 + -0.06666666665 Combine like terms: 0.89690827 + -0.06666666665 = 0.83024160335 x = 0.83024160335 Simplifying x = 0.83024160335Subproblem 2
x + 0.06666666665 = -0.89690827 Simplifying x + 0.06666666665 = -0.89690827 Reorder the terms: 0.06666666665 + x = -0.89690827 Solving 0.06666666665 + x = -0.89690827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06666666665' to each side of the equation. 0.06666666665 + -0.06666666665 + x = -0.89690827 + -0.06666666665 Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000 0.00000000000 + x = -0.89690827 + -0.06666666665 x = -0.89690827 + -0.06666666665 Combine like terms: -0.89690827 + -0.06666666665 = -0.96357493665 x = -0.96357493665 Simplifying x = -0.96357493665Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.83024160335, -0.96357493665}
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