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Simplifying 16x2 + 75x + 3 = 0 Reorder the terms: 3 + 75x + 16x2 = 0 Solving 3 + 75x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.1875 + 4.6875x + x2 = 0 Move the constant term to the right: Add '-0.1875' to each side of the equation. 0.1875 + 4.6875x + -0.1875 + x2 = 0 + -0.1875 Reorder the terms: 0.1875 + -0.1875 + 4.6875x + x2 = 0 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + 4.6875x + x2 = 0 + -0.1875 4.6875x + x2 = 0 + -0.1875 Combine like terms: 0 + -0.1875 = -0.1875 4.6875x + x2 = -0.1875 The x term is 4.6875x. Take half its coefficient (2.34375). Square it (5.493164063) and add it to both sides. Add '5.493164063' to each side of the equation. 4.6875x + 5.493164063 + x2 = -0.1875 + 5.493164063 Reorder the terms: 5.493164063 + 4.6875x + x2 = -0.1875 + 5.493164063 Combine like terms: -0.1875 + 5.493164063 = 5.305664063 5.493164063 + 4.6875x + x2 = 5.305664063 Factor a perfect square on the left side: (x + 2.34375)(x + 2.34375) = 5.305664063 Calculate the square root of the right side: 2.303402714 Break this problem into two subproblems by setting (x + 2.34375) equal to 2.303402714 and -2.303402714.Subproblem 1
x + 2.34375 = 2.303402714 Simplifying x + 2.34375 = 2.303402714 Reorder the terms: 2.34375 + x = 2.303402714 Solving 2.34375 + x = 2.303402714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.34375' to each side of the equation. 2.34375 + -2.34375 + x = 2.303402714 + -2.34375 Combine like terms: 2.34375 + -2.34375 = 0.00000 0.00000 + x = 2.303402714 + -2.34375 x = 2.303402714 + -2.34375 Combine like terms: 2.303402714 + -2.34375 = -0.040347286 x = -0.040347286 Simplifying x = -0.040347286Subproblem 2
x + 2.34375 = -2.303402714 Simplifying x + 2.34375 = -2.303402714 Reorder the terms: 2.34375 + x = -2.303402714 Solving 2.34375 + x = -2.303402714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.34375' to each side of the equation. 2.34375 + -2.34375 + x = -2.303402714 + -2.34375 Combine like terms: 2.34375 + -2.34375 = 0.00000 0.00000 + x = -2.303402714 + -2.34375 x = -2.303402714 + -2.34375 Combine like terms: -2.303402714 + -2.34375 = -4.647152714 x = -4.647152714 Simplifying x = -4.647152714Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.040347286, -4.647152714}
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