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Simplifying 2x2 + 59x + 3 = 0 Reorder the terms: 3 + 59x + 2x2 = 0 Solving 3 + 59x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 29.5x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 29.5x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 29.5x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 29.5x + x2 = 0 + -1.5 29.5x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 29.5x + x2 = -1.5 The x term is 29.5x. Take half its coefficient (14.75). Square it (217.5625) and add it to both sides. Add '217.5625' to each side of the equation. 29.5x + 217.5625 + x2 = -1.5 + 217.5625 Reorder the terms: 217.5625 + 29.5x + x2 = -1.5 + 217.5625 Combine like terms: -1.5 + 217.5625 = 216.0625 217.5625 + 29.5x + x2 = 216.0625 Factor a perfect square on the left side: (x + 14.75)(x + 14.75) = 216.0625 Calculate the square root of the right side: 14.699064596 Break this problem into two subproblems by setting (x + 14.75) equal to 14.699064596 and -14.699064596.Subproblem 1
x + 14.75 = 14.699064596 Simplifying x + 14.75 = 14.699064596 Reorder the terms: 14.75 + x = 14.699064596 Solving 14.75 + x = 14.699064596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.75' to each side of the equation. 14.75 + -14.75 + x = 14.699064596 + -14.75 Combine like terms: 14.75 + -14.75 = 0.00 0.00 + x = 14.699064596 + -14.75 x = 14.699064596 + -14.75 Combine like terms: 14.699064596 + -14.75 = -0.050935404 x = -0.050935404 Simplifying x = -0.050935404Subproblem 2
x + 14.75 = -14.699064596 Simplifying x + 14.75 = -14.699064596 Reorder the terms: 14.75 + x = -14.699064596 Solving 14.75 + x = -14.699064596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.75' to each side of the equation. 14.75 + -14.75 + x = -14.699064596 + -14.75 Combine like terms: 14.75 + -14.75 = 0.00 0.00 + x = -14.699064596 + -14.75 x = -14.699064596 + -14.75 Combine like terms: -14.699064596 + -14.75 = -29.449064596 x = -29.449064596 Simplifying x = -29.449064596Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.050935404, -29.449064596}
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