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Simplifying 3x2 + 4x = 78 Reorder the terms: 4x + 3x2 = 78 Solving 4x + 3x2 = 78 Solving for variable 'x'. Reorder the terms: -78 + 4x + 3x2 = 78 + -78 Combine like terms: 78 + -78 = 0 -78 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -26 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + 1.333333333x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + 1.333333333x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 1.333333333x + x2 = 0 + 26 1.333333333x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 1.333333333x + x2 = 26 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 = 26 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 26 + 0.4444444442 Combine like terms: 26 + 0.4444444442 = 26.4444444442 0.4444444442 + 1.333333333x + x2 = 26.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 26.4444444442 Calculate the square root of the right side: 5.142416207 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 5.142416207 and -5.142416207.Subproblem 1
x + 0.6666666665 = 5.142416207 Simplifying x + 0.6666666665 = 5.142416207 Reorder the terms: 0.6666666665 + x = 5.142416207 Solving 0.6666666665 + x = 5.142416207 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 = 5.142416207 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 5.142416207 + -0.6666666665 x = 5.142416207 + -0.6666666665 Combine like terms: 5.142416207 + -0.6666666665 = 4.4757495405 x = 4.4757495405 Simplifying x = 4.4757495405Subproblem 2
x + 0.6666666665 = -5.142416207 Simplifying x + 0.6666666665 = -5.142416207 Reorder the terms: 0.6666666665 + x = -5.142416207 Solving 0.6666666665 + x = -5.142416207 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 = -5.142416207 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -5.142416207 + -0.6666666665 x = -5.142416207 + -0.6666666665 Combine like terms: -5.142416207 + -0.6666666665 = -5.8090828735 x = -5.8090828735 Simplifying x = -5.8090828735Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.4757495405, -5.8090828735}
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