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Simplifying -30x + x * x = -37 Multiply x * x -30x + x2 = -37 Solving -30x + x2 = -37 Solving for variable 'x'. Reorder the terms: 37 + -30x + x2 = -37 + 37 Combine like terms: -37 + 37 = 0 37 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + -30x + -37 + x2 = 0 + -37 Reorder the terms: 37 + -37 + -30x + x2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + -30x + x2 = 0 + -37 -30x + x2 = 0 + -37 Combine like terms: 0 + -37 = -37 -30x + x2 = -37 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -37 + 225 Reorder the terms: 225 + -30x + x2 = -37 + 225 Combine like terms: -37 + 225 = 188 225 + -30x + x2 = 188 Factor a perfect square on the left side: (x + -15)(x + -15) = 188 Calculate the square root of the right side: 13.711309201 Break this problem into two subproblems by setting (x + -15) equal to 13.711309201 and -13.711309201.Subproblem 1
x + -15 = 13.711309201 Simplifying x + -15 = 13.711309201 Reorder the terms: -15 + x = 13.711309201 Solving -15 + x = 13.711309201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 13.711309201 + 15 Combine like terms: -15 + 15 = 0 0 + x = 13.711309201 + 15 x = 13.711309201 + 15 Combine like terms: 13.711309201 + 15 = 28.711309201 x = 28.711309201 Simplifying x = 28.711309201Subproblem 2
x + -15 = -13.711309201 Simplifying x + -15 = -13.711309201 Reorder the terms: -15 + x = -13.711309201 Solving -15 + x = -13.711309201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -13.711309201 + 15 Combine like terms: -15 + 15 = 0 0 + x = -13.711309201 + 15 x = -13.711309201 + 15 Combine like terms: -13.711309201 + 15 = 1.288690799 x = 1.288690799 Simplifying x = 1.288690799Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.711309201, 1.288690799}
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