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Simplifying 3x2 + 6x + 5 = 308 Reorder the terms: 5 + 6x + 3x2 = 308 Solving 5 + 6x + 3x2 = 308 Solving for variable 'x'. Reorder the terms: 5 + -308 + 6x + 3x2 = 308 + -308 Combine like terms: 5 + -308 = -303 -303 + 6x + 3x2 = 308 + -308 Combine like terms: 308 + -308 = 0 -303 + 6x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-101 + 2x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-101 + 2x + x2)' equal to zero and attempt to solve: Simplifying -101 + 2x + x2 = 0 Solving -101 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '101' to each side of the equation. -101 + 2x + 101 + x2 = 0 + 101 Reorder the terms: -101 + 101 + 2x + x2 = 0 + 101 Combine like terms: -101 + 101 = 0 0 + 2x + x2 = 0 + 101 2x + x2 = 0 + 101 Combine like terms: 0 + 101 = 101 2x + x2 = 101 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 101 + 1 Reorder the terms: 1 + 2x + x2 = 101 + 1 Combine like terms: 101 + 1 = 102 1 + 2x + x2 = 102 Factor a perfect square on the left side: (x + 1)(x + 1) = 102 Calculate the square root of the right side: 10.099504938 Break this problem into two subproblems by setting (x + 1) equal to 10.099504938 and -10.099504938.Subproblem 1
x + 1 = 10.099504938 Simplifying x + 1 = 10.099504938 Reorder the terms: 1 + x = 10.099504938 Solving 1 + x = 10.099504938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 10.099504938 + -1 Combine like terms: 1 + -1 = 0 0 + x = 10.099504938 + -1 x = 10.099504938 + -1 Combine like terms: 10.099504938 + -1 = 9.099504938 x = 9.099504938 Simplifying x = 9.099504938Subproblem 2
x + 1 = -10.099504938 Simplifying x + 1 = -10.099504938 Reorder the terms: 1 + x = -10.099504938 Solving 1 + x = -10.099504938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -10.099504938 + -1 Combine like terms: 1 + -1 = 0 0 + x = -10.099504938 + -1 x = -10.099504938 + -1 Combine like terms: -10.099504938 + -1 = -11.099504938 x = -11.099504938 Simplifying x = -11.099504938Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.099504938, -11.099504938}Solution
x = {9.099504938, -11.099504938}
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