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Simplifying 0 = 300x + -5x2 + -5 Reorder the terms: 0 = -5 + 300x + -5x2 Solving 0 = -5 + 300x + -5x2 Solving for variable 'x'. Combine like terms: 0 + 5 = 5 5 + -300x + 5x2 = -5 + 300x + -5x2 + 5 + -300x + 5x2 Reorder the terms: 5 + -300x + 5x2 = -5 + 5 + 300x + -300x + -5x2 + 5x2 Combine like terms: -5 + 5 = 0 5 + -300x + 5x2 = 0 + 300x + -300x + -5x2 + 5x2 5 + -300x + 5x2 = 300x + -300x + -5x2 + 5x2 Combine like terms: 300x + -300x = 0 5 + -300x + 5x2 = 0 + -5x2 + 5x2 5 + -300x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 5 + -300x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + -60x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -60x + x2)' equal to zero and attempt to solve: Simplifying 1 + -60x + x2 = 0 Solving 1 + -60x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -60x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -60x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -60x + x2 = 0 + -1 -60x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -60x + x2 = -1 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = -1 + 900 Reorder the terms: 900 + -60x + x2 = -1 + 900 Combine like terms: -1 + 900 = 899 900 + -60x + x2 = 899 Factor a perfect square on the left side: (x + -30)(x + -30) = 899 Calculate the square root of the right side: 29.983328701 Break this problem into two subproblems by setting (x + -30) equal to 29.983328701 and -29.983328701.Subproblem 1
x + -30 = 29.983328701 Simplifying x + -30 = 29.983328701 Reorder the terms: -30 + x = 29.983328701 Solving -30 + x = 29.983328701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 29.983328701 + 30 Combine like terms: -30 + 30 = 0 0 + x = 29.983328701 + 30 x = 29.983328701 + 30 Combine like terms: 29.983328701 + 30 = 59.983328701 x = 59.983328701 Simplifying x = 59.983328701Subproblem 2
x + -30 = -29.983328701 Simplifying x + -30 = -29.983328701 Reorder the terms: -30 + x = -29.983328701 Solving -30 + x = -29.983328701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -29.983328701 + 30 Combine like terms: -30 + 30 = 0 0 + x = -29.983328701 + 30 x = -29.983328701 + 30 Combine like terms: -29.983328701 + 30 = 0.016671299 x = 0.016671299 Simplifying x = 0.016671299Solution
The solution to the problem is based on the solutions from the subproblems. x = {59.983328701, 0.016671299}Solution
x = {59.983328701, 0.016671299}
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