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Simplifying 3x2 + 6x + 20 = 2531 Reorder the terms: 20 + 6x + 3x2 = 2531 Solving 20 + 6x + 3x2 = 2531 Solving for variable 'x'. Reorder the terms: 20 + -2531 + 6x + 3x2 = 2531 + -2531 Combine like terms: 20 + -2531 = -2511 -2511 + 6x + 3x2 = 2531 + -2531 Combine like terms: 2531 + -2531 = 0 -2511 + 6x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-837 + 2x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-837 + 2x + x2)' equal to zero and attempt to solve: Simplifying -837 + 2x + x2 = 0 Solving -837 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '837' to each side of the equation. -837 + 2x + 837 + x2 = 0 + 837 Reorder the terms: -837 + 837 + 2x + x2 = 0 + 837 Combine like terms: -837 + 837 = 0 0 + 2x + x2 = 0 + 837 2x + x2 = 0 + 837 Combine like terms: 0 + 837 = 837 2x + x2 = 837 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 = 837 + 1 Reorder the terms: 1 + 2x + x2 = 837 + 1 Combine like terms: 837 + 1 = 838 1 + 2x + x2 = 838 Factor a perfect square on the left side: (x + 1)(x + 1) = 838 Calculate the square root of the right side: 28.948229652 Break this problem into two subproblems by setting (x + 1) equal to 28.948229652 and -28.948229652.Subproblem 1
x + 1 = 28.948229652 Simplifying x + 1 = 28.948229652 Reorder the terms: 1 + x = 28.948229652 Solving 1 + x = 28.948229652 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 = 28.948229652 + -1 Combine like terms: 1 + -1 = 0 0 + x = 28.948229652 + -1 x = 28.948229652 + -1 Combine like terms: 28.948229652 + -1 = 27.948229652 x = 27.948229652 Simplifying x = 27.948229652Subproblem 2
x + 1 = -28.948229652 Simplifying x + 1 = -28.948229652 Reorder the terms: 1 + x = -28.948229652 Solving 1 + x = -28.948229652 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 = -28.948229652 + -1 Combine like terms: 1 + -1 = 0 0 + x = -28.948229652 + -1 x = -28.948229652 + -1 Combine like terms: -28.948229652 + -1 = -29.948229652 x = -29.948229652 Simplifying x = -29.948229652Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.948229652, -29.948229652}Solution
x = {27.948229652, -29.948229652}
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