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Simplifying 6000x2 + 6000x + -11000 = 0 Reorder the terms: -11000 + 6000x + 6000x2 = 0 Solving -11000 + 6000x + 6000x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '1000'. 1000(-11 + 6x + 6x2) = 0 Ignore the factor 1000.Subproblem 1
Set the factor '(-11 + 6x + 6x2)' equal to zero and attempt to solve: Simplifying -11 + 6x + 6x2 = 0 Solving -11 + 6x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.833333333 + x + x2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + x + 1.833333333 + x2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + x + x2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + x + x2 = 0 + 1.833333333 x + x2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 x + x2 = 1.833333333 The x term is x. 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. + 0.25 + x2 = 1.833333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.833333333 + 0.25 Combine like terms: 1.833333333 + 0.25 = 2.083333333 1.25 + x2 = 2.083333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.083333333 Calculate the square root of the right side: 1.443375673 Break this problem into two subproblems by setting (x + 0.5) equal to 1.443375673 and -1.443375673.Subproblem 1
x + 0.5 = 1.443375673 Simplifying x + 0.5 = 1.443375673 Reorder the terms: 0.5 + x = 1.443375673 Solving 0.5 + x = 1.443375673 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 = 1.443375673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.443375673 + -0.5 x = 1.443375673 + -0.5 Combine like terms: 1.443375673 + -0.5 = 0.943375673 x = 0.943375673 Simplifying x = 0.943375673Subproblem 2
x + 0.5 = -1.443375673 Simplifying x + 0.5 = -1.443375673 Reorder the terms: 0.5 + x = -1.443375673 Solving 0.5 + x = -1.443375673 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 = -1.443375673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.443375673 + -0.5 x = -1.443375673 + -0.5 Combine like terms: -1.443375673 + -0.5 = -1.943375673 x = -1.943375673 Simplifying x = -1.943375673Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.943375673, -1.943375673}Solution
x = {0.943375673, -1.943375673}
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