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Simplifying 2x2 + 30x = 1000 Reorder the terms: 30x + 2x2 = 1000 Solving 30x + 2x2 = 1000 Solving for variable 'x'. Reorder the terms: -1000 + 30x + 2x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -1000 + 30x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-500 + 15x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-500 + 15x + x2)' equal to zero and attempt to solve: Simplifying -500 + 15x + x2 = 0 Solving -500 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '500' to each side of the equation. -500 + 15x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + 15x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + 15x + x2 = 0 + 500 15x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 15x + x2 = 500 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 500 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 500 + 56.25 Combine like terms: 500 + 56.25 = 556.25 56.25 + 15x + x2 = 556.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 556.25 Calculate the square root of the right side: 23.58495283 Break this problem into two subproblems by setting (x + 7.5) equal to 23.58495283 and -23.58495283.Subproblem 1
x + 7.5 = 23.58495283 Simplifying x + 7.5 = 23.58495283 Reorder the terms: 7.5 + x = 23.58495283 Solving 7.5 + x = 23.58495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 23.58495283 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 23.58495283 + -7.5 x = 23.58495283 + -7.5 Combine like terms: 23.58495283 + -7.5 = 16.08495283 x = 16.08495283 Simplifying x = 16.08495283Subproblem 2
x + 7.5 = -23.58495283 Simplifying x + 7.5 = -23.58495283 Reorder the terms: 7.5 + x = -23.58495283 Solving 7.5 + x = -23.58495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -23.58495283 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -23.58495283 + -7.5 x = -23.58495283 + -7.5 Combine like terms: -23.58495283 + -7.5 = -31.08495283 x = -31.08495283 Simplifying x = -31.08495283Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.08495283, -31.08495283}Solution
x = {16.08495283, -31.08495283}
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