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Simplifying x2 + -10x + -13 = 17 Reorder the terms: -13 + -10x + x2 = 17 Solving -13 + -10x + x2 = 17 Solving for variable 'x'. Reorder the terms: -13 + -17 + -10x + x2 = 17 + -17 Combine like terms: -13 + -17 = -30 -30 + -10x + x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -30 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -10x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -10x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -10x + x2 = 0 + 30 -10x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -10x + x2 = 30 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 30 + 25 Reorder the terms: 25 + -10x + x2 = 30 + 25 Combine like terms: 30 + 25 = 55 25 + -10x + x2 = 55 Factor a perfect square on the left side: (x + -5)(x + -5) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (x + -5) equal to 7.416198487 and -7.416198487.Subproblem 1
x + -5 = 7.416198487 Simplifying x + -5 = 7.416198487 Reorder the terms: -5 + x = 7.416198487 Solving -5 + x = 7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 7.416198487 + 5 Combine like terms: -5 + 5 = 0 0 + x = 7.416198487 + 5 x = 7.416198487 + 5 Combine like terms: 7.416198487 + 5 = 12.416198487 x = 12.416198487 Simplifying x = 12.416198487Subproblem 2
x + -5 = -7.416198487 Simplifying x + -5 = -7.416198487 Reorder the terms: -5 + x = -7.416198487 Solving -5 + x = -7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -7.416198487 + 5 Combine like terms: -5 + 5 = 0 0 + x = -7.416198487 + 5 x = -7.416198487 + 5 Combine like terms: -7.416198487 + 5 = -2.416198487 x = -2.416198487 Simplifying x = -2.416198487Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.416198487, -2.416198487}
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