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Simplifying 6006 + 10x = 10x2 Solving 6006 + 10x = 10x2 Solving for variable 'x'. Combine like terms: 10x2 + -10x2 = 0 6006 + 10x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3003 + 5x + -5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3003 + 5x + -5x2)' equal to zero and attempt to solve: Simplifying 3003 + 5x + -5x2 = 0 Solving 3003 + 5x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -600.6 + -1x + x2 = 0 Move the constant term to the right: Add '600.6' to each side of the equation. -600.6 + -1x + 600.6 + x2 = 0 + 600.6 Reorder the terms: -600.6 + 600.6 + -1x + x2 = 0 + 600.6 Combine like terms: -600.6 + 600.6 = 0.0 0.0 + -1x + x2 = 0 + 600.6 -1x + x2 = 0 + 600.6 Combine like terms: 0 + 600.6 = 600.6 -1x + x2 = 600.6 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 600.6 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 600.6 + 0.25 Combine like terms: 600.6 + 0.25 = 600.85 0.25 + -1x + x2 = 600.85 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 600.85 Calculate the square root of the right side: 24.51224184 Break this problem into two subproblems by setting (x + -0.5) equal to 24.51224184 and -24.51224184.Subproblem 1
x + -0.5 = 24.51224184 Simplifying x + -0.5 = 24.51224184 Reorder the terms: -0.5 + x = 24.51224184 Solving -0.5 + x = 24.51224184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 24.51224184 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 24.51224184 + 0.5 x = 24.51224184 + 0.5 Combine like terms: 24.51224184 + 0.5 = 25.01224184 x = 25.01224184 Simplifying x = 25.01224184Subproblem 2
x + -0.5 = -24.51224184 Simplifying x + -0.5 = -24.51224184 Reorder the terms: -0.5 + x = -24.51224184 Solving -0.5 + x = -24.51224184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -24.51224184 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -24.51224184 + 0.5 x = -24.51224184 + 0.5 Combine like terms: -24.51224184 + 0.5 = -24.01224184 x = -24.01224184 Simplifying x = -24.01224184Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.01224184, -24.01224184}Solution
x = {25.01224184, -24.01224184}
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