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Simplifying 16(x2) + (44x) + -222 = 0 Reorder the terms: -222 + (44x) + 16x2 = 0 Solving -222 + (44x) + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-111 + (22x) + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-111 + (22x) + 8x2)' equal to zero and attempt to solve: Simplifying -111 + (22x) + 8x2 = 0 Solving -111 + (22x) + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -13.875 + (2.75x) + x2 = 0 Move the constant term to the right: Add '13.875' to each side of the equation. -13.875 + (2.75x) + 13.875 + x2 = 0 + 13.875 Reorder the terms: -13.875 + 13.875 + (2.75x) + x2 = 0 + 13.875 Combine like terms: -13.875 + 13.875 = 0.000 0.000 + (2.75x) + x2 = 0 + 13.875 (2.75x) + x2 = 0 + 13.875 Combine like terms: 0 + 13.875 = 13.875 (2.75x) + x2 = 13.875 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 = 13.875 + 1.890625 Reorder the terms: 1.890625 + (2.75x) + x2 = 13.875 + 1.890625 Combine like terms: 13.875 + 1.890625 = 15.765625 1.890625 + (2.75x) + x2 = 15.765625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 15.765625 Calculate the square root of the right side: 3.970595044 Break this problem into two subproblems by setting (x + 1.375) equal to 3.970595044 and -3.970595044.Subproblem 1
x + 1.375 = 3.970595044 Simplifying x + 1.375 = 3.970595044 Reorder the terms: 1.375 + x = 3.970595044 Solving 1.375 + x = 3.970595044 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 = 3.970595044 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 3.970595044 + -1.375 x = 3.970595044 + -1.375 Combine like terms: 3.970595044 + -1.375 = 2.595595044 x = 2.595595044 Simplifying x = 2.595595044Subproblem 2
x + 1.375 = -3.970595044 Simplifying x + 1.375 = -3.970595044 Reorder the terms: 1.375 + x = -3.970595044 Solving 1.375 + x = -3.970595044 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 = -3.970595044 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -3.970595044 + -1.375 x = -3.970595044 + -1.375 Combine like terms: -3.970595044 + -1.375 = -5.345595044 x = -5.345595044 Simplifying x = -5.345595044Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.595595044, -5.345595044}Solution
x = {2.595595044, -5.345595044}
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