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Simplifying 3x2 + -12.4x + 3 = 0 Reorder the terms: 3 + -12.4x + 3x2 = 0 Solving 3 + -12.4x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + -4.133333333x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4.133333333x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -4.133333333x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4.133333333x + x2 = 0 + -1 -4.133333333x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4.133333333x + x2 = -1 The x term is -4.133333333x. Take half its coefficient (-2.066666667). Square it (4.271111112) and add it to both sides. Add '4.271111112' to each side of the equation. -4.133333333x + 4.271111112 + x2 = -1 + 4.271111112 Reorder the terms: 4.271111112 + -4.133333333x + x2 = -1 + 4.271111112 Combine like terms: -1 + 4.271111112 = 3.271111112 4.271111112 + -4.133333333x + x2 = 3.271111112 Factor a perfect square on the left side: (x + -2.066666667)(x + -2.066666667) = 3.271111112 Calculate the square root of the right side: 1.808621329 Break this problem into two subproblems by setting (x + -2.066666667) equal to 1.808621329 and -1.808621329.Subproblem 1
x + -2.066666667 = 1.808621329 Simplifying x + -2.066666667 = 1.808621329 Reorder the terms: -2.066666667 + x = 1.808621329 Solving -2.066666667 + x = 1.808621329 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.066666667' to each side of the equation. -2.066666667 + 2.066666667 + x = 1.808621329 + 2.066666667 Combine like terms: -2.066666667 + 2.066666667 = 0.000000000 0.000000000 + x = 1.808621329 + 2.066666667 x = 1.808621329 + 2.066666667 Combine like terms: 1.808621329 + 2.066666667 = 3.875287996 x = 3.875287996 Simplifying x = 3.875287996Subproblem 2
x + -2.066666667 = -1.808621329 Simplifying x + -2.066666667 = -1.808621329 Reorder the terms: -2.066666667 + x = -1.808621329 Solving -2.066666667 + x = -1.808621329 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.066666667' to each side of the equation. -2.066666667 + 2.066666667 + x = -1.808621329 + 2.066666667 Combine like terms: -2.066666667 + 2.066666667 = 0.000000000 0.000000000 + x = -1.808621329 + 2.066666667 x = -1.808621329 + 2.066666667 Combine like terms: -1.808621329 + 2.066666667 = 0.258045338 x = 0.258045338 Simplifying x = 0.258045338Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.875287996, 0.258045338}
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