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Simplifying 37x + 12 = 3x2 Reorder the terms: 12 + 37x = 3x2 Solving 12 + 37x = 3x2 Solving for variable 'x'. Combine like terms: 3x2 + -3x2 = 0 12 + 37x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -4 + -12.33333333x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -12.33333333x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -12.33333333x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -12.33333333x + x2 = 0 + 4 -12.33333333x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -12.33333333x + x2 = 4 The x term is -12.33333333x. Take half its coefficient (-6.166666665). Square it (38.02777776) and add it to both sides. Add '38.02777776' to each side of the equation. -12.33333333x + 38.02777776 + x2 = 4 + 38.02777776 Reorder the terms: 38.02777776 + -12.33333333x + x2 = 4 + 38.02777776 Combine like terms: 4 + 38.02777776 = 42.02777776 38.02777776 + -12.33333333x + x2 = 42.02777776 Factor a perfect square on the left side: (x + -6.166666665)(x + -6.166666665) = 42.02777776 Calculate the square root of the right side: 6.482883445 Break this problem into two subproblems by setting (x + -6.166666665) equal to 6.482883445 and -6.482883445.Subproblem 1
x + -6.166666665 = 6.482883445 Simplifying x + -6.166666665 = 6.482883445 Reorder the terms: -6.166666665 + x = 6.482883445 Solving -6.166666665 + x = 6.482883445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.166666665' to each side of the equation. -6.166666665 + 6.166666665 + x = 6.482883445 + 6.166666665 Combine like terms: -6.166666665 + 6.166666665 = 0.000000000 0.000000000 + x = 6.482883445 + 6.166666665 x = 6.482883445 + 6.166666665 Combine like terms: 6.482883445 + 6.166666665 = 12.64955011 x = 12.64955011 Simplifying x = 12.64955011Subproblem 2
x + -6.166666665 = -6.482883445 Simplifying x + -6.166666665 = -6.482883445 Reorder the terms: -6.166666665 + x = -6.482883445 Solving -6.166666665 + x = -6.482883445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.166666665' to each side of the equation. -6.166666665 + 6.166666665 + x = -6.482883445 + 6.166666665 Combine like terms: -6.166666665 + 6.166666665 = 0.000000000 0.000000000 + x = -6.482883445 + 6.166666665 x = -6.482883445 + 6.166666665 Combine like terms: -6.482883445 + 6.166666665 = -0.31621678 x = -0.31621678 Simplifying x = -0.31621678Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.64955011, -0.31621678}
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