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Simplifying 2x2 + 11x + 3 = 0 Reorder the terms: 3 + 11x + 2x2 = 0 Solving 3 + 11x + 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 + 5.5x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 5.5x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 5.5x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 5.5x + x2 = 0 + -1.5 5.5x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 5.5x + x2 = -1.5 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = -1.5 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = -1.5 + 7.5625 Combine like terms: -1.5 + 7.5625 = 6.0625 7.5625 + 5.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + 2.75) equal to 2.46221445 and -2.46221445.Subproblem 1
x + 2.75 = 2.46221445 Simplifying x + 2.75 = 2.46221445 Reorder the terms: 2.75 + x = 2.46221445 Solving 2.75 + x = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 2.46221445 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 2.46221445 + -2.75 x = 2.46221445 + -2.75 Combine like terms: 2.46221445 + -2.75 = -0.28778555 x = -0.28778555 Simplifying x = -0.28778555Subproblem 2
x + 2.75 = -2.46221445 Simplifying x + 2.75 = -2.46221445 Reorder the terms: 2.75 + x = -2.46221445 Solving 2.75 + x = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -2.46221445 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -2.46221445 + -2.75 x = -2.46221445 + -2.75 Combine like terms: -2.46221445 + -2.75 = -5.21221445 x = -5.21221445 Simplifying x = -5.21221445Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.28778555, -5.21221445}
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