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Simplifying -50x * x + 3x + 1000 = 0 Multiply x * x -50x2 + 3x + 1000 = 0 Reorder the terms: 1000 + 3x + -50x2 = 0 Solving 1000 + 3x + -50x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -50 the coefficient of the squared term: Divide each side by '-50'. -20 + -0.06x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -0.06x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -0.06x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -0.06x + x2 = 0 + 20 -0.06x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -0.06x + x2 = 20 The x term is -0.06x. Take half its coefficient (-0.03). Square it (0.0009) and add it to both sides. Add '0.0009' to each side of the equation. -0.06x + 0.0009 + x2 = 20 + 0.0009 Reorder the terms: 0.0009 + -0.06x + x2 = 20 + 0.0009 Combine like terms: 20 + 0.0009 = 20.0009 0.0009 + -0.06x + x2 = 20.0009 Factor a perfect square on the left side: (x + -0.03)(x + -0.03) = 20.0009 Calculate the square root of the right side: 4.472236577 Break this problem into two subproblems by setting (x + -0.03) equal to 4.472236577 and -4.472236577.Subproblem 1
x + -0.03 = 4.472236577 Simplifying x + -0.03 = 4.472236577 Reorder the terms: -0.03 + x = 4.472236577 Solving -0.03 + x = 4.472236577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03' to each side of the equation. -0.03 + 0.03 + x = 4.472236577 + 0.03 Combine like terms: -0.03 + 0.03 = 0.00 0.00 + x = 4.472236577 + 0.03 x = 4.472236577 + 0.03 Combine like terms: 4.472236577 + 0.03 = 4.502236577 x = 4.502236577 Simplifying x = 4.502236577Subproblem 2
x + -0.03 = -4.472236577 Simplifying x + -0.03 = -4.472236577 Reorder the terms: -0.03 + x = -4.472236577 Solving -0.03 + x = -4.472236577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03' to each side of the equation. -0.03 + 0.03 + x = -4.472236577 + 0.03 Combine like terms: -0.03 + 0.03 = 0.00 0.00 + x = -4.472236577 + 0.03 x = -4.472236577 + 0.03 Combine like terms: -4.472236577 + 0.03 = -4.442236577 x = -4.442236577 Simplifying x = -4.442236577Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.502236577, -4.442236577}
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