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Simplifying 3x2 + 4x = 24 Reorder the terms: 4x + 3x2 = 24 Solving 4x + 3x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + 4x + 3x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 1.333333333x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 1.333333333x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 1.333333333x + x2 = 0 + 8 1.333333333x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 1.333333333x + x2 = 8 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 = 8 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 8 + 0.4444444442 Combine like terms: 8 + 0.4444444442 = 8.4444444442 0.4444444442 + 1.333333333x + x2 = 8.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 8.4444444442 Calculate the square root of the right side: 2.905932629 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 2.905932629 and -2.905932629.Subproblem 1
x + 0.6666666665 = 2.905932629 Simplifying x + 0.6666666665 = 2.905932629 Reorder the terms: 0.6666666665 + x = 2.905932629 Solving 0.6666666665 + x = 2.905932629 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 = 2.905932629 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 2.905932629 + -0.6666666665 x = 2.905932629 + -0.6666666665 Combine like terms: 2.905932629 + -0.6666666665 = 2.2392659625 x = 2.2392659625 Simplifying x = 2.2392659625Subproblem 2
x + 0.6666666665 = -2.905932629 Simplifying x + 0.6666666665 = -2.905932629 Reorder the terms: 0.6666666665 + x = -2.905932629 Solving 0.6666666665 + x = -2.905932629 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 = -2.905932629 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -2.905932629 + -0.6666666665 x = -2.905932629 + -0.6666666665 Combine like terms: -2.905932629 + -0.6666666665 = -3.5725992955 x = -3.5725992955 Simplifying x = -3.5725992955Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2392659625, -3.5725992955}
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