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Simplifying 4x2 + 11x + 5 = -4x + 2 Reorder the terms: 5 + 11x + 4x2 = -4x + 2 Reorder the terms: 5 + 11x + 4x2 = 2 + -4x Solving 5 + 11x + 4x2 = 2 + -4x Solving for variable 'x'. Reorder the terms: 5 + -2 + 11x + 4x + 4x2 = 2 + -4x + -2 + 4x Combine like terms: 5 + -2 = 3 3 + 11x + 4x + 4x2 = 2 + -4x + -2 + 4x Combine like terms: 11x + 4x = 15x 3 + 15x + 4x2 = 2 + -4x + -2 + 4x Reorder the terms: 3 + 15x + 4x2 = 2 + -2 + -4x + 4x Combine like terms: 2 + -2 = 0 3 + 15x + 4x2 = 0 + -4x + 4x 3 + 15x + 4x2 = -4x + 4x Combine like terms: -4x + 4x = 0 3 + 15x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 3.75x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 3.75x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 3.75x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 3.75x + x2 = 0 + -0.75 3.75x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 3.75x + x2 = -0.75 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = -0.75 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = -0.75 + 3.515625 Combine like terms: -0.75 + 3.515625 = 2.765625 3.515625 + 3.75x + x2 = 2.765625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 2.765625 Calculate the square root of the right side: 1.663016837 Break this problem into two subproblems by setting (x + 1.875) equal to 1.663016837 and -1.663016837.Subproblem 1
x + 1.875 = 1.663016837 Simplifying x + 1.875 = 1.663016837 Reorder the terms: 1.875 + x = 1.663016837 Solving 1.875 + x = 1.663016837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 1.663016837 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 1.663016837 + -1.875 x = 1.663016837 + -1.875 Combine like terms: 1.663016837 + -1.875 = -0.211983163 x = -0.211983163 Simplifying x = -0.211983163Subproblem 2
x + 1.875 = -1.663016837 Simplifying x + 1.875 = -1.663016837 Reorder the terms: 1.875 + x = -1.663016837 Solving 1.875 + x = -1.663016837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -1.663016837 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -1.663016837 + -1.875 x = -1.663016837 + -1.875 Combine like terms: -1.663016837 + -1.875 = -3.538016837 x = -3.538016837 Simplifying x = -3.538016837Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.211983163, -3.538016837}
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