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Simplifying 11x2 + 14x + -5 = 0 Reorder the terms: -5 + 14x + 11x2 = 0 Solving -5 + 14x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.4545454545 + 1.272727273x + x2 = 0 Move the constant term to the right: Add '0.4545454545' to each side of the equation. -0.4545454545 + 1.272727273x + 0.4545454545 + x2 = 0 + 0.4545454545 Reorder the terms: -0.4545454545 + 0.4545454545 + 1.272727273x + x2 = 0 + 0.4545454545 Combine like terms: -0.4545454545 + 0.4545454545 = 0.0000000000 0.0000000000 + 1.272727273x + x2 = 0 + 0.4545454545 1.272727273x + x2 = 0 + 0.4545454545 Combine like terms: 0 + 0.4545454545 = 0.4545454545 1.272727273x + x2 = 0.4545454545 The x term is 1.272727273x. Take half its coefficient (0.6363636365). Square it (0.4049586779) and add it to both sides. Add '0.4049586779' to each side of the equation. 1.272727273x + 0.4049586779 + x2 = 0.4545454545 + 0.4049586779 Reorder the terms: 0.4049586779 + 1.272727273x + x2 = 0.4545454545 + 0.4049586779 Combine like terms: 0.4545454545 + 0.4049586779 = 0.8595041324 0.4049586779 + 1.272727273x + x2 = 0.8595041324 Factor a perfect square on the left side: (x + 0.6363636365)(x + 0.6363636365) = 0.8595041324 Calculate the square root of the right side: 0.927094457 Break this problem into two subproblems by setting (x + 0.6363636365) equal to 0.927094457 and -0.927094457.Subproblem 1
x + 0.6363636365 = 0.927094457 Simplifying x + 0.6363636365 = 0.927094457 Reorder the terms: 0.6363636365 + x = 0.927094457 Solving 0.6363636365 + x = 0.927094457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6363636365' to each side of the equation. 0.6363636365 + -0.6363636365 + x = 0.927094457 + -0.6363636365 Combine like terms: 0.6363636365 + -0.6363636365 = 0.0000000000 0.0000000000 + x = 0.927094457 + -0.6363636365 x = 0.927094457 + -0.6363636365 Combine like terms: 0.927094457 + -0.6363636365 = 0.2907308205 x = 0.2907308205 Simplifying x = 0.2907308205Subproblem 2
x + 0.6363636365 = -0.927094457 Simplifying x + 0.6363636365 = -0.927094457 Reorder the terms: 0.6363636365 + x = -0.927094457 Solving 0.6363636365 + x = -0.927094457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6363636365' to each side of the equation. 0.6363636365 + -0.6363636365 + x = -0.927094457 + -0.6363636365 Combine like terms: 0.6363636365 + -0.6363636365 = 0.0000000000 0.0000000000 + x = -0.927094457 + -0.6363636365 x = -0.927094457 + -0.6363636365 Combine like terms: -0.927094457 + -0.6363636365 = -1.5634580935 x = -1.5634580935 Simplifying x = -1.5634580935Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2907308205, -1.5634580935}
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