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Simplifying 6x + 2x2 = 102 Solving 6x + 2x2 = 102 Solving for variable 'x'. Reorder the terms: -102 + 6x + 2x2 = 102 + -102 Combine like terms: 102 + -102 = 0 -102 + 6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-51 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-51 + 3x + x2)' equal to zero and attempt to solve: Simplifying -51 + 3x + x2 = 0 Solving -51 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + 3x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + 3x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + 3x + x2 = 0 + 51 3x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 3x + x2 = 51 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 51 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 51 + 2.25 Combine like terms: 51 + 2.25 = 53.25 2.25 + 3x + x2 = 53.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 53.25 Calculate the square root of the right side: 7.29725976 Break this problem into two subproblems by setting (x + 1.5) equal to 7.29725976 and -7.29725976.Subproblem 1
x + 1.5 = 7.29725976 Simplifying x + 1.5 = 7.29725976 Reorder the terms: 1.5 + x = 7.29725976 Solving 1.5 + x = 7.29725976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 7.29725976 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.29725976 + -1.5 x = 7.29725976 + -1.5 Combine like terms: 7.29725976 + -1.5 = 5.79725976 x = 5.79725976 Simplifying x = 5.79725976Subproblem 2
x + 1.5 = -7.29725976 Simplifying x + 1.5 = -7.29725976 Reorder the terms: 1.5 + x = -7.29725976 Solving 1.5 + x = -7.29725976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -7.29725976 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.29725976 + -1.5 x = -7.29725976 + -1.5 Combine like terms: -7.29725976 + -1.5 = -8.79725976 x = -8.79725976 Simplifying x = -8.79725976Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.79725976, -8.79725976}Solution
x = {5.79725976, -8.79725976}
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