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Simplifying 4x + 3x2 = 180 Solving 4x + 3x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 4x + 3x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -60 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 1.333333333x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 1.333333333x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 1.333333333x + x2 = 0 + 60 1.333333333x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 1.333333333x + x2 = 60 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 60 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 60 + 0.4444444442 Combine like terms: 60 + 0.4444444442 = 60.4444444442 0.4444444442 + 1.333333333x + x2 = 60.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 60.4444444442 Calculate the square root of the right side: 7.774602526 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 7.774602526 and -7.774602526.Subproblem 1
x + 0.6666666665 = 7.774602526 Simplifying x + 0.6666666665 = 7.774602526 Reorder the terms: 0.6666666665 + x = 7.774602526 Solving 0.6666666665 + x = 7.774602526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 7.774602526 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 7.774602526 + -0.6666666665 x = 7.774602526 + -0.6666666665 Combine like terms: 7.774602526 + -0.6666666665 = 7.1079358595 x = 7.1079358595 Simplifying x = 7.1079358595Subproblem 2
x + 0.6666666665 = -7.774602526 Simplifying x + 0.6666666665 = -7.774602526 Reorder the terms: 0.6666666665 + x = -7.774602526 Solving 0.6666666665 + x = -7.774602526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -7.774602526 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -7.774602526 + -0.6666666665 x = -7.774602526 + -0.6666666665 Combine like terms: -7.774602526 + -0.6666666665 = -8.4412691925 x = -8.4412691925 Simplifying x = -8.4412691925Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.1079358595, -8.4412691925}
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