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Simplifying x2 + -21x + -1000 = 0 Reorder the terms: -1000 + -21x + x2 = 0 Solving -1000 + -21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -21x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -21x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -21x + x2 = 0 + 1000 -21x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -21x + x2 = 1000 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = 1000 + 110.25 Reorder the terms: 110.25 + -21x + x2 = 1000 + 110.25 Combine like terms: 1000 + 110.25 = 1110.25 110.25 + -21x + x2 = 1110.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 1110.25 Calculate the square root of the right side: 33.320414163 Break this problem into two subproblems by setting (x + -10.5) equal to 33.320414163 and -33.320414163.Subproblem 1
x + -10.5 = 33.320414163 Simplifying x + -10.5 = 33.320414163 Reorder the terms: -10.5 + x = 33.320414163 Solving -10.5 + x = 33.320414163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 33.320414163 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 33.320414163 + 10.5 x = 33.320414163 + 10.5 Combine like terms: 33.320414163 + 10.5 = 43.820414163 x = 43.820414163 Simplifying x = 43.820414163Subproblem 2
x + -10.5 = -33.320414163 Simplifying x + -10.5 = -33.320414163 Reorder the terms: -10.5 + x = -33.320414163 Solving -10.5 + x = -33.320414163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -33.320414163 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -33.320414163 + 10.5 x = -33.320414163 + 10.5 Combine like terms: -33.320414163 + 10.5 = -22.820414163 x = -22.820414163 Simplifying x = -22.820414163Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.820414163, -22.820414163}
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