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Simplifying 3x2 + 4x + -8 = 112 Reorder the terms: -8 + 4x + 3x2 = 112 Solving -8 + 4x + 3x2 = 112 Solving for variable 'x'. Reorder the terms: -8 + -112 + 4x + 3x2 = 112 + -112 Combine like terms: -8 + -112 = -120 -120 + 4x + 3x2 = 112 + -112 Combine like terms: 112 + -112 = 0 -120 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -40 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 1.333333333x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 1.333333333x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 1.333333333x + x2 = 0 + 40 1.333333333x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 1.333333333x + x2 = 40 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 = 40 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 40 + 0.4444444442 Combine like terms: 40 + 0.4444444442 = 40.4444444442 0.4444444442 + 1.333333333x + x2 = 40.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 40.4444444442 Calculate the square root of the right side: 6.359594676 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 6.359594676 and -6.359594676.Subproblem 1
x + 0.6666666665 = 6.359594676 Simplifying x + 0.6666666665 = 6.359594676 Reorder the terms: 0.6666666665 + x = 6.359594676 Solving 0.6666666665 + x = 6.359594676 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 = 6.359594676 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 6.359594676 + -0.6666666665 x = 6.359594676 + -0.6666666665 Combine like terms: 6.359594676 + -0.6666666665 = 5.6929280095 x = 5.6929280095 Simplifying x = 5.6929280095Subproblem 2
x + 0.6666666665 = -6.359594676 Simplifying x + 0.6666666665 = -6.359594676 Reorder the terms: 0.6666666665 + x = -6.359594676 Solving 0.6666666665 + x = -6.359594676 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 = -6.359594676 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -6.359594676 + -0.6666666665 x = -6.359594676 + -0.6666666665 Combine like terms: -6.359594676 + -0.6666666665 = -7.0262613425 x = -7.0262613425 Simplifying x = -7.0262613425Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.6929280095, -7.0262613425}
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