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Simplifying (9x + 40) = 3x2 Reorder the terms: (40 + 9x) = 3x2 Remove parenthesis around (40 + 9x) 40 + 9x = 3x2 Solving 40 + 9x = 3x2 Solving for variable 'x'. Combine like terms: 3x2 + -3x2 = 0 40 + 9x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -13.33333333 + -3x + x2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + -3x + 13.33333333 + x2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + -3x + x2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + -3x + x2 = 0 + 13.33333333 -3x + x2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 -3x + x2 = 13.33333333 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 13.33333333 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 13.33333333 + 2.25 Combine like terms: 13.33333333 + 2.25 = 15.58333333 2.25 + -3x + x2 = 15.58333333 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 15.58333333 Calculate the square root of the right side: 3.947573094 Break this problem into two subproblems by setting (x + -1.5) equal to 3.947573094 and -3.947573094.Subproblem 1
x + -1.5 = 3.947573094 Simplifying x + -1.5 = 3.947573094 Reorder the terms: -1.5 + x = 3.947573094 Solving -1.5 + x = 3.947573094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.947573094 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.947573094 + 1.5 x = 3.947573094 + 1.5 Combine like terms: 3.947573094 + 1.5 = 5.447573094 x = 5.447573094 Simplifying x = 5.447573094Subproblem 2
x + -1.5 = -3.947573094 Simplifying x + -1.5 = -3.947573094 Reorder the terms: -1.5 + x = -3.947573094 Solving -1.5 + x = -3.947573094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.947573094 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.947573094 + 1.5 x = -3.947573094 + 1.5 Combine like terms: -3.947573094 + 1.5 = -2.447573094 x = -2.447573094 Simplifying x = -2.447573094Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.447573094, -2.447573094}
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