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Simplifying x2 + 10x + -45 = 0 Reorder the terms: -45 + 10x + x2 = 0 Solving -45 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 10x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 10x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 10x + x2 = 0 + 45 10x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 10x + x2 = 45 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 = 45 + 25 Reorder the terms: 25 + 10x + x2 = 45 + 25 Combine like terms: 45 + 25 = 70 25 + 10x + x2 = 70 Factor a perfect square on the left side: (x + 5)(x + 5) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (x + 5) equal to 8.366600265 and -8.366600265.Subproblem 1
x + 5 = 8.366600265 Simplifying x + 5 = 8.366600265 Reorder the terms: 5 + x = 8.366600265 Solving 5 + x = 8.366600265 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 = 8.366600265 + -5 Combine like terms: 5 + -5 = 0 0 + x = 8.366600265 + -5 x = 8.366600265 + -5 Combine like terms: 8.366600265 + -5 = 3.366600265 x = 3.366600265 Simplifying x = 3.366600265Subproblem 2
x + 5 = -8.366600265 Simplifying x + 5 = -8.366600265 Reorder the terms: 5 + x = -8.366600265 Solving 5 + x = -8.366600265 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 = -8.366600265 + -5 Combine like terms: 5 + -5 = 0 0 + x = -8.366600265 + -5 x = -8.366600265 + -5 Combine like terms: -8.366600265 + -5 = -13.366600265 x = -13.366600265 Simplifying x = -13.366600265Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.366600265, -13.366600265}
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