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Simplifying x2 + 20x + -312 = 0 Reorder the terms: -312 + 20x + x2 = 0 Solving -312 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '312' to each side of the equation. -312 + 20x + 312 + x2 = 0 + 312 Reorder the terms: -312 + 312 + 20x + x2 = 0 + 312 Combine like terms: -312 + 312 = 0 0 + 20x + x2 = 0 + 312 20x + x2 = 0 + 312 Combine like terms: 0 + 312 = 312 20x + x2 = 312 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 312 + 100 Reorder the terms: 100 + 20x + x2 = 312 + 100 Combine like terms: 312 + 100 = 412 100 + 20x + x2 = 412 Factor a perfect square on the left side: (x + 10)(x + 10) = 412 Calculate the square root of the right side: 20.29778313 Break this problem into two subproblems by setting (x + 10) equal to 20.29778313 and -20.29778313.Subproblem 1
x + 10 = 20.29778313 Simplifying x + 10 = 20.29778313 Reorder the terms: 10 + x = 20.29778313 Solving 10 + x = 20.29778313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 20.29778313 + -10 Combine like terms: 10 + -10 = 0 0 + x = 20.29778313 + -10 x = 20.29778313 + -10 Combine like terms: 20.29778313 + -10 = 10.29778313 x = 10.29778313 Simplifying x = 10.29778313Subproblem 2
x + 10 = -20.29778313 Simplifying x + 10 = -20.29778313 Reorder the terms: 10 + x = -20.29778313 Solving 10 + x = -20.29778313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -20.29778313 + -10 Combine like terms: 10 + -10 = 0 0 + x = -20.29778313 + -10 x = -20.29778313 + -10 Combine like terms: -20.29778313 + -10 = -30.29778313 x = -30.29778313 Simplifying x = -30.29778313Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.29778313, -30.29778313}
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