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Simplifying 3x2 + 300x + -3000 = 0 Reorder the terms: -3000 + 300x + 3x2 = 0 Solving -3000 + 300x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1000 + 100x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1000 + 100x + x2)' equal to zero and attempt to solve: Simplifying -1000 + 100x + x2 = 0 Solving -1000 + 100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 100x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 100x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 100x + x2 = 0 + 1000 100x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 100x + x2 = 1000 The x term is 100x. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x + 2500 + x2 = 1000 + 2500 Reorder the terms: 2500 + 100x + x2 = 1000 + 2500 Combine like terms: 1000 + 2500 = 3500 2500 + 100x + x2 = 3500 Factor a perfect square on the left side: (x + 50)(x + 50) = 3500 Calculate the square root of the right side: 59.160797831 Break this problem into two subproblems by setting (x + 50) equal to 59.160797831 and -59.160797831.Subproblem 1
x + 50 = 59.160797831 Simplifying x + 50 = 59.160797831 Reorder the terms: 50 + x = 59.160797831 Solving 50 + x = 59.160797831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 59.160797831 + -50 Combine like terms: 50 + -50 = 0 0 + x = 59.160797831 + -50 x = 59.160797831 + -50 Combine like terms: 59.160797831 + -50 = 9.160797831 x = 9.160797831 Simplifying x = 9.160797831Subproblem 2
x + 50 = -59.160797831 Simplifying x + 50 = -59.160797831 Reorder the terms: 50 + x = -59.160797831 Solving 50 + x = -59.160797831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -59.160797831 + -50 Combine like terms: 50 + -50 = 0 0 + x = -59.160797831 + -50 x = -59.160797831 + -50 Combine like terms: -59.160797831 + -50 = -109.160797831 x = -109.160797831 Simplifying x = -109.160797831Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.160797831, -109.160797831}Solution
x = {9.160797831, -109.160797831}
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