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Simplifying 8x2 + 22x + 2 = 0 Reorder the terms: 2 + 22x + 8x2 = 0 Solving 2 + 22x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 11x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 11x + 4x2)' equal to zero and attempt to solve: Simplifying 1 + 11x + 4x2 = 0 Solving 1 + 11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 2.75x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 2.75x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 2.75x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 2.75x + x2 = 0 + -0.25 2.75x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 2.75x + x2 = -0.25 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 = -0.25 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = -0.25 + 1.890625 Combine like terms: -0.25 + 1.890625 = 1.640625 1.890625 + 2.75x + x2 = 1.640625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (x + 1.375) equal to 1.280868846 and -1.280868846.Subproblem 1
x + 1.375 = 1.280868846 Simplifying x + 1.375 = 1.280868846 Reorder the terms: 1.375 + x = 1.280868846 Solving 1.375 + x = 1.280868846 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 = 1.280868846 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 1.280868846 + -1.375 x = 1.280868846 + -1.375 Combine like terms: 1.280868846 + -1.375 = -0.094131154 x = -0.094131154 Simplifying x = -0.094131154Subproblem 2
x + 1.375 = -1.280868846 Simplifying x + 1.375 = -1.280868846 Reorder the terms: 1.375 + x = -1.280868846 Solving 1.375 + x = -1.280868846 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 = -1.280868846 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -1.280868846 + -1.375 x = -1.280868846 + -1.375 Combine like terms: -1.280868846 + -1.375 = -2.655868846 x = -2.655868846 Simplifying x = -2.655868846Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.094131154, -2.655868846}Solution
x = {-0.094131154, -2.655868846}
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