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Simplifying 0 = 4x2 + 11x + 4 Reorder the terms: 0 = 4 + 11x + 4x2 Solving 0 = 4 + 11x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -11x + -4x2 = 4 + 11x + 4x2 + -4 + -11x + -4x2 Reorder the terms: -4 + -11x + -4x2 = 4 + -4 + 11x + -11x + 4x2 + -4x2 Combine like terms: 4 + -4 = 0 -4 + -11x + -4x2 = 0 + 11x + -11x + 4x2 + -4x2 -4 + -11x + -4x2 = 11x + -11x + 4x2 + -4x2 Combine like terms: 11x + -11x = 0 -4 + -11x + -4x2 = 0 + 4x2 + -4x2 -4 + -11x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -4 + -11x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 11x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 11x + 4x2)' equal to zero and attempt to solve: Simplifying 4 + 11x + 4x2 = 0 Solving 4 + 11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + 2.75x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.75x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 2.75x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.75x + x2 = 0 + -1 2.75x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.75x + x2 = -1 The x term is 2.75x. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75x + 1.890625 + x2 = -1 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = -1 + 1.890625 Combine like terms: -1 + 1.890625 = 0.890625 1.890625 + 2.75x + x2 = 0.890625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (x + 1.375) equal to 0.943729304 and -0.943729304.Subproblem 1
x + 1.375 = 0.943729304 Simplifying x + 1.375 = 0.943729304 Reorder the terms: 1.375 + x = 0.943729304 Solving 1.375 + x = 0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 0.943729304 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 0.943729304 + -1.375 x = 0.943729304 + -1.375 Combine like terms: 0.943729304 + -1.375 = -0.431270696 x = -0.431270696 Simplifying x = -0.431270696Subproblem 2
x + 1.375 = -0.943729304 Simplifying x + 1.375 = -0.943729304 Reorder the terms: 1.375 + x = -0.943729304 Solving 1.375 + x = -0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -0.943729304 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -0.943729304 + -1.375 x = -0.943729304 + -1.375 Combine like terms: -0.943729304 + -1.375 = -2.318729304 x = -2.318729304 Simplifying x = -2.318729304Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.431270696, -2.318729304}Solution
x = {-0.431270696, -2.318729304}
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