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Simplifying 4.9x2 + -17x + -23 = 0 Reorder the terms: -23 + -17x + 4.9x2 = 0 Solving -23 + -17x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -4.693877551 + -3.469387755x + x2 = 0 Move the constant term to the right: Add '4.693877551' to each side of the equation. -4.693877551 + -3.469387755x + 4.693877551 + x2 = 0 + 4.693877551 Reorder the terms: -4.693877551 + 4.693877551 + -3.469387755x + x2 = 0 + 4.693877551 Combine like terms: -4.693877551 + 4.693877551 = 0.000000000 0.000000000 + -3.469387755x + x2 = 0 + 4.693877551 -3.469387755x + x2 = 0 + 4.693877551 Combine like terms: 0 + 4.693877551 = 4.693877551 -3.469387755x + x2 = 4.693877551 The x term is -3.469387755x. Take half its coefficient (-1.734693878). Square it (3.009162850) and add it to both sides. Add '3.009162850' to each side of the equation. -3.469387755x + 3.009162850 + x2 = 4.693877551 + 3.009162850 Reorder the terms: 3.009162850 + -3.469387755x + x2 = 4.693877551 + 3.009162850 Combine like terms: 4.693877551 + 3.009162850 = 7.703040401 3.009162850 + -3.469387755x + x2 = 7.703040401 Factor a perfect square on the left side: (x + -1.734693878)(x + -1.734693878) = 7.703040401 Calculate the square root of the right side: 2.775435173 Break this problem into two subproblems by setting (x + -1.734693878) equal to 2.775435173 and -2.775435173.Subproblem 1
x + -1.734693878 = 2.775435173 Simplifying x + -1.734693878 = 2.775435173 Reorder the terms: -1.734693878 + x = 2.775435173 Solving -1.734693878 + x = 2.775435173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.734693878' to each side of the equation. -1.734693878 + 1.734693878 + x = 2.775435173 + 1.734693878 Combine like terms: -1.734693878 + 1.734693878 = 0.000000000 0.000000000 + x = 2.775435173 + 1.734693878 x = 2.775435173 + 1.734693878 Combine like terms: 2.775435173 + 1.734693878 = 4.510129051 x = 4.510129051 Simplifying x = 4.510129051Subproblem 2
x + -1.734693878 = -2.775435173 Simplifying x + -1.734693878 = -2.775435173 Reorder the terms: -1.734693878 + x = -2.775435173 Solving -1.734693878 + x = -2.775435173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.734693878' to each side of the equation. -1.734693878 + 1.734693878 + x = -2.775435173 + 1.734693878 Combine like terms: -1.734693878 + 1.734693878 = 0.000000000 0.000000000 + x = -2.775435173 + 1.734693878 x = -2.775435173 + 1.734693878 Combine like terms: -2.775435173 + 1.734693878 = -1.040741295 x = -1.040741295 Simplifying x = -1.040741295Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.510129051, -1.040741295}
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