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Simplifying 3x2 + 4x = 360 Reorder the terms: 4x + 3x2 = 360 Solving 4x + 3x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 4x + 3x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -120 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 1.333333333x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 1.333333333x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 1.333333333x + x2 = 0 + 120 1.333333333x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 1.333333333x + x2 = 120 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 = 120 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 120 + 0.4444444442 Combine like terms: 120 + 0.4444444442 = 120.4444444442 0.4444444442 + 1.333333333x + x2 = 120.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 120.4444444442 Calculate the square root of the right side: 10.974718422 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 10.974718422 and -10.974718422.Subproblem 1
x + 0.6666666665 = 10.974718422 Simplifying x + 0.6666666665 = 10.974718422 Reorder the terms: 0.6666666665 + x = 10.974718422 Solving 0.6666666665 + x = 10.974718422 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 = 10.974718422 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 10.974718422 + -0.6666666665 x = 10.974718422 + -0.6666666665 Combine like terms: 10.974718422 + -0.6666666665 = 10.3080517555 x = 10.3080517555 Simplifying x = 10.3080517555Subproblem 2
x + 0.6666666665 = -10.974718422 Simplifying x + 0.6666666665 = -10.974718422 Reorder the terms: 0.6666666665 + x = -10.974718422 Solving 0.6666666665 + x = -10.974718422 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 = -10.974718422 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -10.974718422 + -0.6666666665 x = -10.974718422 + -0.6666666665 Combine like terms: -10.974718422 + -0.6666666665 = -11.6413850885 x = -11.6413850885 Simplifying x = -11.6413850885Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.3080517555, -11.6413850885}
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