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Simplifying x(27 + x) + (-33 + 4x) = 870 (27 * x + x * x) + (-33 + 4x) = 870 (27x + x2) + (-33 + 4x) = 870 Remove parenthesis around (-33 + 4x) 27x + x2 + -33 + 4x = 870 Reorder the terms: -33 + 27x + 4x + x2 = 870 Combine like terms: 27x + 4x = 31x -33 + 31x + x2 = 870 Solving -33 + 31x + x2 = 870 Solving for variable 'x'. Reorder the terms: -33 + -870 + 31x + x2 = 870 + -870 Combine like terms: -33 + -870 = -903 -903 + 31x + x2 = 870 + -870 Combine like terms: 870 + -870 = 0 -903 + 31x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '903' to each side of the equation. -903 + 31x + 903 + x2 = 0 + 903 Reorder the terms: -903 + 903 + 31x + x2 = 0 + 903 Combine like terms: -903 + 903 = 0 0 + 31x + x2 = 0 + 903 31x + x2 = 0 + 903 Combine like terms: 0 + 903 = 903 31x + x2 = 903 The x term is 31x. Take half its coefficient (15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. 31x + 240.25 + x2 = 903 + 240.25 Reorder the terms: 240.25 + 31x + x2 = 903 + 240.25 Combine like terms: 903 + 240.25 = 1143.25 240.25 + 31x + x2 = 1143.25 Factor a perfect square on the left side: (x + 15.5)(x + 15.5) = 1143.25 Calculate the square root of the right side: 33.811980125 Break this problem into two subproblems by setting (x + 15.5) equal to 33.811980125 and -33.811980125.Subproblem 1
x + 15.5 = 33.811980125 Simplifying x + 15.5 = 33.811980125 Reorder the terms: 15.5 + x = 33.811980125 Solving 15.5 + x = 33.811980125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = 33.811980125 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = 33.811980125 + -15.5 x = 33.811980125 + -15.5 Combine like terms: 33.811980125 + -15.5 = 18.311980125 x = 18.311980125 Simplifying x = 18.311980125Subproblem 2
x + 15.5 = -33.811980125 Simplifying x + 15.5 = -33.811980125 Reorder the terms: 15.5 + x = -33.811980125 Solving 15.5 + x = -33.811980125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = -33.811980125 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = -33.811980125 + -15.5 x = -33.811980125 + -15.5 Combine like terms: -33.811980125 + -15.5 = -49.311980125 x = -49.311980125 Simplifying x = -49.311980125Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.311980125, -49.311980125}
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