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Simplifying 23x2 + 26x + -17 = 0 Reorder the terms: -17 + 26x + 23x2 = 0 Solving -17 + 26x + 23x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. -0.7391304348 + 1.130434783x + x2 = 0 Move the constant term to the right: Add '0.7391304348' to each side of the equation. -0.7391304348 + 1.130434783x + 0.7391304348 + x2 = 0 + 0.7391304348 Reorder the terms: -0.7391304348 + 0.7391304348 + 1.130434783x + x2 = 0 + 0.7391304348 Combine like terms: -0.7391304348 + 0.7391304348 = 0.0000000000 0.0000000000 + 1.130434783x + x2 = 0 + 0.7391304348 1.130434783x + x2 = 0 + 0.7391304348 Combine like terms: 0 + 0.7391304348 = 0.7391304348 1.130434783x + x2 = 0.7391304348 The x term is 1.130434783x. Take half its coefficient (0.5652173915). Square it (0.3194706997) and add it to both sides. Add '0.3194706997' to each side of the equation. 1.130434783x + 0.3194706997 + x2 = 0.7391304348 + 0.3194706997 Reorder the terms: 0.3194706997 + 1.130434783x + x2 = 0.7391304348 + 0.3194706997 Combine like terms: 0.7391304348 + 0.3194706997 = 1.0586011345 0.3194706997 + 1.130434783x + x2 = 1.0586011345 Factor a perfect square on the left side: (x + 0.5652173915)(x + 0.5652173915) = 1.0586011345 Calculate the square root of the right side: 1.028883441 Break this problem into two subproblems by setting (x + 0.5652173915) equal to 1.028883441 and -1.028883441.Subproblem 1
x + 0.5652173915 = 1.028883441 Simplifying x + 0.5652173915 = 1.028883441 Reorder the terms: 0.5652173915 + x = 1.028883441 Solving 0.5652173915 + x = 1.028883441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5652173915' to each side of the equation. 0.5652173915 + -0.5652173915 + x = 1.028883441 + -0.5652173915 Combine like terms: 0.5652173915 + -0.5652173915 = 0.0000000000 0.0000000000 + x = 1.028883441 + -0.5652173915 x = 1.028883441 + -0.5652173915 Combine like terms: 1.028883441 + -0.5652173915 = 0.4636660495 x = 0.4636660495 Simplifying x = 0.4636660495Subproblem 2
x + 0.5652173915 = -1.028883441 Simplifying x + 0.5652173915 = -1.028883441 Reorder the terms: 0.5652173915 + x = -1.028883441 Solving 0.5652173915 + x = -1.028883441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5652173915' to each side of the equation. 0.5652173915 + -0.5652173915 + x = -1.028883441 + -0.5652173915 Combine like terms: 0.5652173915 + -0.5652173915 = 0.0000000000 0.0000000000 + x = -1.028883441 + -0.5652173915 x = -1.028883441 + -0.5652173915 Combine like terms: -1.028883441 + -0.5652173915 = -1.5941008325 x = -1.5941008325 Simplifying x = -1.5941008325Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4636660495, -1.5941008325}
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