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Simplifying 3x2 + 4x + -420 = 0 Reorder the terms: -420 + 4x + 3x2 = 0 Solving -420 + 4x + 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'. -140 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + 1.333333333x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 1.333333333x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 1.333333333x + x2 = 0 + 140 1.333333333x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 1.333333333x + x2 = 140 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 = 140 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 140 + 0.4444444442 Combine like terms: 140 + 0.4444444442 = 140.4444444442 0.4444444442 + 1.333333333x + x2 = 140.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 140.4444444442 Calculate the square root of the right side: 11.85092589 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 11.85092589 and -11.85092589.Subproblem 1
x + 0.6666666665 = 11.85092589 Simplifying x + 0.6666666665 = 11.85092589 Reorder the terms: 0.6666666665 + x = 11.85092589 Solving 0.6666666665 + x = 11.85092589 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 = 11.85092589 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 11.85092589 + -0.6666666665 x = 11.85092589 + -0.6666666665 Combine like terms: 11.85092589 + -0.6666666665 = 11.1842592235 x = 11.1842592235 Simplifying x = 11.1842592235Subproblem 2
x + 0.6666666665 = -11.85092589 Simplifying x + 0.6666666665 = -11.85092589 Reorder the terms: 0.6666666665 + x = -11.85092589 Solving 0.6666666665 + x = -11.85092589 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 = -11.85092589 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -11.85092589 + -0.6666666665 x = -11.85092589 + -0.6666666665 Combine like terms: -11.85092589 + -0.6666666665 = -12.5175925565 x = -12.5175925565 Simplifying x = -12.5175925565Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.1842592235, -12.5175925565}
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