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Simplifying 3x2 + 6x + 5 = 440 Reorder the terms: 5 + 6x + 3x2 = 440 Solving 5 + 6x + 3x2 = 440 Solving for variable 'x'. Reorder the terms: 5 + -440 + 6x + 3x2 = 440 + -440 Combine like terms: 5 + -440 = -435 -435 + 6x + 3x2 = 440 + -440 Combine like terms: 440 + -440 = 0 -435 + 6x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-145 + 2x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-145 + 2x + x2)' equal to zero and attempt to solve: Simplifying -145 + 2x + x2 = 0 Solving -145 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '145' to each side of the equation. -145 + 2x + 145 + x2 = 0 + 145 Reorder the terms: -145 + 145 + 2x + x2 = 0 + 145 Combine like terms: -145 + 145 = 0 0 + 2x + x2 = 0 + 145 2x + x2 = 0 + 145 Combine like terms: 0 + 145 = 145 2x + x2 = 145 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 = 145 + 1 Reorder the terms: 1 + 2x + x2 = 145 + 1 Combine like terms: 145 + 1 = 146 1 + 2x + x2 = 146 Factor a perfect square on the left side: (x + 1)(x + 1) = 146 Calculate the square root of the right side: 12.083045974 Break this problem into two subproblems by setting (x + 1) equal to 12.083045974 and -12.083045974.Subproblem 1
x + 1 = 12.083045974 Simplifying x + 1 = 12.083045974 Reorder the terms: 1 + x = 12.083045974 Solving 1 + x = 12.083045974 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 = 12.083045974 + -1 Combine like terms: 1 + -1 = 0 0 + x = 12.083045974 + -1 x = 12.083045974 + -1 Combine like terms: 12.083045974 + -1 = 11.083045974 x = 11.083045974 Simplifying x = 11.083045974Subproblem 2
x + 1 = -12.083045974 Simplifying x + 1 = -12.083045974 Reorder the terms: 1 + x = -12.083045974 Solving 1 + x = -12.083045974 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 = -12.083045974 + -1 Combine like terms: 1 + -1 = 0 0 + x = -12.083045974 + -1 x = -12.083045974 + -1 Combine like terms: -12.083045974 + -1 = -13.083045974 x = -13.083045974 Simplifying x = -13.083045974Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.083045974, -13.083045974}Solution
x = {11.083045974, -13.083045974}
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