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Simplifying x2 + -3x + -21150 = 0 Reorder the terms: -21150 + -3x + x2 = 0 Solving -21150 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '21150' to each side of the equation. -21150 + -3x + 21150 + x2 = 0 + 21150 Reorder the terms: -21150 + 21150 + -3x + x2 = 0 + 21150 Combine like terms: -21150 + 21150 = 0 0 + -3x + x2 = 0 + 21150 -3x + x2 = 0 + 21150 Combine like terms: 0 + 21150 = 21150 -3x + x2 = 21150 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 21150 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 21150 + 2.25 Combine like terms: 21150 + 2.25 = 21152.25 2.25 + -3x + x2 = 21152.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 21152.25 Calculate the square root of the right side: 145.438131176 Break this problem into two subproblems by setting (x + -1.5) equal to 145.438131176 and -145.438131176.Subproblem 1
x + -1.5 = 145.438131176 Simplifying x + -1.5 = 145.438131176 Reorder the terms: -1.5 + x = 145.438131176 Solving -1.5 + x = 145.438131176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 145.438131176 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 145.438131176 + 1.5 x = 145.438131176 + 1.5 Combine like terms: 145.438131176 + 1.5 = 146.938131176 x = 146.938131176 Simplifying x = 146.938131176Subproblem 2
x + -1.5 = -145.438131176 Simplifying x + -1.5 = -145.438131176 Reorder the terms: -1.5 + x = -145.438131176 Solving -1.5 + x = -145.438131176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -145.438131176 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -145.438131176 + 1.5 x = -145.438131176 + 1.5 Combine like terms: -145.438131176 + 1.5 = -143.938131176 x = -143.938131176 Simplifying x = -143.938131176Solution
The solution to the problem is based on the solutions from the subproblems. x = {146.938131176, -143.938131176}
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