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Simplifying 3x2 + -34x + 87 = 0 Reorder the terms: 87 + -34x + 3x2 = 0 Solving 87 + -34x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 29 + -11.33333333x + x2 = 0 Move the constant term to the right: Add '-29' to each side of the equation. 29 + -11.33333333x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + -11.33333333x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -11.33333333x + x2 = 0 + -29 -11.33333333x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 -11.33333333x + x2 = -29 The x term is -11.33333333x. Take half its coefficient (-5.666666665). Square it (32.11111109) and add it to both sides. Add '32.11111109' to each side of the equation. -11.33333333x + 32.11111109 + x2 = -29 + 32.11111109 Reorder the terms: 32.11111109 + -11.33333333x + x2 = -29 + 32.11111109 Combine like terms: -29 + 32.11111109 = 3.11111109 32.11111109 + -11.33333333x + x2 = 3.11111109 Factor a perfect square on the left side: (x + -5.666666665)(x + -5.666666665) = 3.11111109 Calculate the square root of the right side: 1.763834201 Break this problem into two subproblems by setting (x + -5.666666665) equal to 1.763834201 and -1.763834201.Subproblem 1
x + -5.666666665 = 1.763834201 Simplifying x + -5.666666665 = 1.763834201 Reorder the terms: -5.666666665 + x = 1.763834201 Solving -5.666666665 + x = 1.763834201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.666666665' to each side of the equation. -5.666666665 + 5.666666665 + x = 1.763834201 + 5.666666665 Combine like terms: -5.666666665 + 5.666666665 = 0.000000000 0.000000000 + x = 1.763834201 + 5.666666665 x = 1.763834201 + 5.666666665 Combine like terms: 1.763834201 + 5.666666665 = 7.430500866 x = 7.430500866 Simplifying x = 7.430500866Subproblem 2
x + -5.666666665 = -1.763834201 Simplifying x + -5.666666665 = -1.763834201 Reorder the terms: -5.666666665 + x = -1.763834201 Solving -5.666666665 + x = -1.763834201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.666666665' to each side of the equation. -5.666666665 + 5.666666665 + x = -1.763834201 + 5.666666665 Combine like terms: -5.666666665 + 5.666666665 = 0.000000000 0.000000000 + x = -1.763834201 + 5.666666665 x = -1.763834201 + 5.666666665 Combine like terms: -1.763834201 + 5.666666665 = 3.902832464 x = 3.902832464 Simplifying x = 3.902832464Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.430500866, 3.902832464}
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