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Simplifying (5x2) + -1(6x) + -1(2) = 0 Remove parenthesis around (6x) (5x2) + -1 * 6x + -1(2) = 0 Multiply -1 * 6 (5x2) + -6x + -1(2) = 0 Multiply -1 * 2 (5x2) + -6x + -2 = 0 Reorder the terms: -2 + -6x + (5x2) = 0 Solving -2 + -6x + (5x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -1.2x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -1.2x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -1.2x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -1.2x + x2 = 0 + 0.4 -1.2x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -1.2x + x2 = 0.4 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 0.4 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 0.4 + 0.36 Combine like terms: 0.4 + 0.36 = 0.76 0.36 + -1.2x + x2 = 0.76 Factor a perfect square on the left side: ((x) + -0.6)((x) + -0.6) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting ((x) + -0.6) equal to 0.871779789 and -0.871779789.Subproblem 1
(x) + -0.6 = 0.871779789 Simplifying (x) + -0.6 = 0.871779789 x + -0.6 = 0.871779789 Reorder the terms: -0.6 + x = 0.871779789 Solving -0.6 + x = 0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.871779789 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.871779789 + 0.6 x = 0.871779789 + 0.6 Combine like terms: 0.871779789 + 0.6 = 1.471779789 x = 1.471779789 Simplifying x = 1.471779789Subproblem 2
(x) + -0.6 = -0.871779789 Simplifying (x) + -0.6 = -0.871779789 x + -0.6 = -0.871779789 Reorder the terms: -0.6 + x = -0.871779789 Solving -0.6 + x = -0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -0.871779789 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.871779789 + 0.6 x = -0.871779789 + 0.6 Combine like terms: -0.871779789 + 0.6 = -0.271779789 x = -0.271779789 Simplifying x = -0.271779789Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.471779789, -0.271779789}
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