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Simplifying -4x2 + -17x + 384 = 0 Reorder the terms: 384 + -17x + -4x2 = 0 Solving 384 + -17x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -96 + 4.25x + x2 = 0 Move the constant term to the right: Add '96' to each side of the equation. -96 + 4.25x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + 4.25x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 4.25x + x2 = 0 + 96 4.25x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 4.25x + x2 = 96 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = 96 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = 96 + 4.515625 Combine like terms: 96 + 4.515625 = 100.515625 4.515625 + 4.25x + x2 = 100.515625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 100.515625 Calculate the square root of the right side: 10.025748102 Break this problem into two subproblems by setting (x + 2.125) equal to 10.025748102 and -10.025748102.Subproblem 1
x + 2.125 = 10.025748102 Simplifying x + 2.125 = 10.025748102 Reorder the terms: 2.125 + x = 10.025748102 Solving 2.125 + x = 10.025748102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 10.025748102 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 10.025748102 + -2.125 x = 10.025748102 + -2.125 Combine like terms: 10.025748102 + -2.125 = 7.900748102 x = 7.900748102 Simplifying x = 7.900748102Subproblem 2
x + 2.125 = -10.025748102 Simplifying x + 2.125 = -10.025748102 Reorder the terms: 2.125 + x = -10.025748102 Solving 2.125 + x = -10.025748102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -10.025748102 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -10.025748102 + -2.125 x = -10.025748102 + -2.125 Combine like terms: -10.025748102 + -2.125 = -12.150748102 x = -12.150748102 Simplifying x = -12.150748102Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.900748102, -12.150748102}
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