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Simplifying 4x(x + -17) = 103 Reorder the terms: 4x(-17 + x) = 103 (-17 * 4x + x * 4x) = 103 (-68x + 4x2) = 103 Solving -68x + 4x2 = 103 Solving for variable 'x'. Reorder the terms: -103 + -68x + 4x2 = 103 + -103 Combine like terms: 103 + -103 = 0 -103 + -68x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -25.75 + -17x + x2 = 0 Move the constant term to the right: Add '25.75' to each side of the equation. -25.75 + -17x + 25.75 + x2 = 0 + 25.75 Reorder the terms: -25.75 + 25.75 + -17x + x2 = 0 + 25.75 Combine like terms: -25.75 + 25.75 = 0.00 0.00 + -17x + x2 = 0 + 25.75 -17x + x2 = 0 + 25.75 Combine like terms: 0 + 25.75 = 25.75 -17x + x2 = 25.75 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = 25.75 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 25.75 + 72.25 Combine like terms: 25.75 + 72.25 = 98 72.25 + -17x + x2 = 98 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (x + -8.5) equal to 9.899494937 and -9.899494937.Subproblem 1
x + -8.5 = 9.899494937 Simplifying x + -8.5 = 9.899494937 Reorder the terms: -8.5 + x = 9.899494937 Solving -8.5 + x = 9.899494937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 9.899494937 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 9.899494937 + 8.5 x = 9.899494937 + 8.5 Combine like terms: 9.899494937 + 8.5 = 18.399494937 x = 18.399494937 Simplifying x = 18.399494937Subproblem 2
x + -8.5 = -9.899494937 Simplifying x + -8.5 = -9.899494937 Reorder the terms: -8.5 + x = -9.899494937 Solving -8.5 + x = -9.899494937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -9.899494937 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -9.899494937 + 8.5 x = -9.899494937 + 8.5 Combine like terms: -9.899494937 + 8.5 = -1.399494937 x = -1.399494937 Simplifying x = -1.399494937Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.399494937, -1.399494937}
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