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Simplifying 9x + 37 = x2 + 3 Reorder the terms: 37 + 9x = x2 + 3 Reorder the terms: 37 + 9x = 3 + x2 Solving 37 + 9x = 3 + x2 Solving for variable 'x'. Reorder the terms: 37 + -3 + 9x + -1x2 = 3 + x2 + -3 + -1x2 Combine like terms: 37 + -3 = 34 34 + 9x + -1x2 = 3 + x2 + -3 + -1x2 Reorder the terms: 34 + 9x + -1x2 = 3 + -3 + x2 + -1x2 Combine like terms: 3 + -3 = 0 34 + 9x + -1x2 = 0 + x2 + -1x2 34 + 9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 34 + 9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -34 + -9x + x2 = 0 Move the constant term to the right: Add '34' to each side of the equation. -34 + -9x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + -9x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + -9x + x2 = 0 + 34 -9x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 -9x + x2 = 34 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 34 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 34 + 20.25 Combine like terms: 34 + 20.25 = 54.25 20.25 + -9x + x2 = 54.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (x + -4.5) equal to 7.365459931 and -7.365459931.Subproblem 1
x + -4.5 = 7.365459931 Simplifying x + -4.5 = 7.365459931 Reorder the terms: -4.5 + x = 7.365459931 Solving -4.5 + x = 7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 7.365459931 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 7.365459931 + 4.5 x = 7.365459931 + 4.5 Combine like terms: 7.365459931 + 4.5 = 11.865459931 x = 11.865459931 Simplifying x = 11.865459931Subproblem 2
x + -4.5 = -7.365459931 Simplifying x + -4.5 = -7.365459931 Reorder the terms: -4.5 + x = -7.365459931 Solving -4.5 + x = -7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -7.365459931 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -7.365459931 + 4.5 x = -7.365459931 + 4.5 Combine like terms: -7.365459931 + 4.5 = -2.865459931 x = -2.865459931 Simplifying x = -2.865459931Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.865459931, -2.865459931}
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