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Simplifying x2 + 6x = -4x2 + 2 Reorder the terms: 6x + x2 = -4x2 + 2 Reorder the terms: 6x + x2 = 2 + -4x2 Solving 6x + x2 = 2 + -4x2 Solving for variable 'x'. Reorder the terms: -2 + 6x + x2 + 4x2 = 2 + -4x2 + -2 + 4x2 Combine like terms: x2 + 4x2 = 5x2 -2 + 6x + 5x2 = 2 + -4x2 + -2 + 4x2 Reorder the terms: -2 + 6x + 5x2 = 2 + -2 + -4x2 + 4x2 Combine like terms: 2 + -2 = 0 -2 + 6x + 5x2 = 0 + -4x2 + 4x2 -2 + 6x + 5x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -2 + 6x + 5x2 = 0 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 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 = 0.271779789Subproblem 2
x + 0.6 = -0.871779789 Simplifying 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 = -1.471779789Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.271779789, -1.471779789}
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