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Simplifying 5x2 + 36x + 2 = 0 Reorder the terms: 2 + 36x + 5x2 = 0 Solving 2 + 36x + 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 + 7.2x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 7.2x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 7.2x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 7.2x + x2 = 0 + -0.4 7.2x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 7.2x + x2 = -0.4 The x term is 7.2x. Take half its coefficient (3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. 7.2x + 12.96 + x2 = -0.4 + 12.96 Reorder the terms: 12.96 + 7.2x + x2 = -0.4 + 12.96 Combine like terms: -0.4 + 12.96 = 12.56 12.96 + 7.2x + x2 = 12.56 Factor a perfect square on the left side: (x + 3.6)(x + 3.6) = 12.56 Calculate the square root of the right side: 3.544009029 Break this problem into two subproblems by setting (x + 3.6) equal to 3.544009029 and -3.544009029.Subproblem 1
x + 3.6 = 3.544009029 Simplifying x + 3.6 = 3.544009029 Reorder the terms: 3.6 + x = 3.544009029 Solving 3.6 + x = 3.544009029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + x = 3.544009029 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + x = 3.544009029 + -3.6 x = 3.544009029 + -3.6 Combine like terms: 3.544009029 + -3.6 = -0.055990971 x = -0.055990971 Simplifying x = -0.055990971Subproblem 2
x + 3.6 = -3.544009029 Simplifying x + 3.6 = -3.544009029 Reorder the terms: 3.6 + x = -3.544009029 Solving 3.6 + x = -3.544009029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + x = -3.544009029 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + x = -3.544009029 + -3.6 x = -3.544009029 + -3.6 Combine like terms: -3.544009029 + -3.6 = -7.144009029 x = -7.144009029 Simplifying x = -7.144009029Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.055990971, -7.144009029}
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