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Simplifying -1(x2 + -10x + -45) = 0 Reorder the terms: -1(-45 + -10x + x2) = 0 (-45 * -1 + -10x * -1 + x2 * -1) = 0 (45 + 10x + -1x2) = 0 Solving 45 + 10x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -45 + -10x + x2 = 0 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 = 13.366600265 x = 13.366600265 Simplifying x = 13.366600265Subproblem 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 = -3.366600265 x = -3.366600265 Simplifying x = -3.366600265Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.366600265, -3.366600265}
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