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Simplifying -0.62x + 0.15x2 = 0.03 Solving -0.62x + 0.15x2 = 0.03 Solving for variable 'x'. Reorder the terms: -0.03 + -0.62x + 0.15x2 = 0.03 + -0.03 Combine like terms: 0.03 + -0.03 = 0.00 -0.03 + -0.62x + 0.15x2 = 0.00 Begin completing the square. Divide all terms by 0.15 the coefficient of the squared term: Divide each side by '0.15'. -0.2 + -4.133333333x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -4.133333333x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -4.133333333x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -4.133333333x + x2 = 0 + 0.2 -4.133333333x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -4.133333333x + x2 = 0.2 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 = 0.2 + 4.271111112 Reorder the terms: 4.271111112 + -4.133333333x + x2 = 0.2 + 4.271111112 Combine like terms: 0.2 + 4.271111112 = 4.471111112 4.271111112 + -4.133333333x + x2 = 4.471111112 Factor a perfect square on the left side: (x + -2.066666667)(x + -2.066666667) = 4.471111112 Calculate the square root of the right side: 2.114500204 Break this problem into two subproblems by setting (x + -2.066666667) equal to 2.114500204 and -2.114500204.Subproblem 1
x + -2.066666667 = 2.114500204 Simplifying x + -2.066666667 = 2.114500204 Reorder the terms: -2.066666667 + x = 2.114500204 Solving -2.066666667 + x = 2.114500204 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 = 2.114500204 + 2.066666667 Combine like terms: -2.066666667 + 2.066666667 = 0.000000000 0.000000000 + x = 2.114500204 + 2.066666667 x = 2.114500204 + 2.066666667 Combine like terms: 2.114500204 + 2.066666667 = 4.181166871 x = 4.181166871 Simplifying x = 4.181166871Subproblem 2
x + -2.066666667 = -2.114500204 Simplifying x + -2.066666667 = -2.114500204 Reorder the terms: -2.066666667 + x = -2.114500204 Solving -2.066666667 + x = -2.114500204 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 = -2.114500204 + 2.066666667 Combine like terms: -2.066666667 + 2.066666667 = 0.000000000 0.000000000 + x = -2.114500204 + 2.066666667 x = -2.114500204 + 2.066666667 Combine like terms: -2.114500204 + 2.066666667 = -0.047833537 x = -0.047833537 Simplifying x = -0.047833537Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.181166871, -0.047833537}
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