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Simplifying x(x + -3) = 4228 Reorder the terms: x(-3 + x) = 4228 (-3 * x + x * x) = 4228 (-3x + x2) = 4228 Solving -3x + x2 = 4228 Solving for variable 'x'. Reorder the terms: -4228 + -3x + x2 = 4228 + -4228 Combine like terms: 4228 + -4228 = 0 -4228 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4228' to each side of the equation. -4228 + -3x + 4228 + x2 = 0 + 4228 Reorder the terms: -4228 + 4228 + -3x + x2 = 0 + 4228 Combine like terms: -4228 + 4228 = 0 0 + -3x + x2 = 0 + 4228 -3x + x2 = 0 + 4228 Combine like terms: 0 + 4228 = 4228 -3x + x2 = 4228 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 = 4228 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 4228 + 2.25 Combine like terms: 4228 + 2.25 = 4230.25 2.25 + -3x + x2 = 4230.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 4230.25 Calculate the square root of the right side: 65.040372078 Break this problem into two subproblems by setting (x + -1.5) equal to 65.040372078 and -65.040372078.Subproblem 1
x + -1.5 = 65.040372078 Simplifying x + -1.5 = 65.040372078 Reorder the terms: -1.5 + x = 65.040372078 Solving -1.5 + x = 65.040372078 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 = 65.040372078 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 65.040372078 + 1.5 x = 65.040372078 + 1.5 Combine like terms: 65.040372078 + 1.5 = 66.540372078 x = 66.540372078 Simplifying x = 66.540372078Subproblem 2
x + -1.5 = -65.040372078 Simplifying x + -1.5 = -65.040372078 Reorder the terms: -1.5 + x = -65.040372078 Solving -1.5 + x = -65.040372078 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 = -65.040372078 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -65.040372078 + 1.5 x = -65.040372078 + 1.5 Combine like terms: -65.040372078 + 1.5 = -63.540372078 x = -63.540372078 Simplifying x = -63.540372078Solution
The solution to the problem is based on the solutions from the subproblems. x = {66.540372078, -63.540372078}
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