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Simplifying 3x2 + -4x = 243 Reorder the terms: -4x + 3x2 = 243 Solving -4x + 3x2 = 243 Solving for variable 'x'. Reorder the terms: -243 + -4x + 3x2 = 243 + -243 Combine like terms: 243 + -243 = 0 -243 + -4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -81 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '81' to each side of the equation. -81 + -1.333333333x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + -1.333333333x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -1.333333333x + x2 = 0 + 81 -1.333333333x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 -1.333333333x + x2 = 81 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 = 81 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 81 + 0.4444444442 Combine like terms: 81 + 0.4444444442 = 81.4444444442 0.4444444442 + -1.333333333x + x2 = 81.4444444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 81.4444444442 Calculate the square root of the right side: 9.02465758 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 9.02465758 and -9.02465758.Subproblem 1
x + -0.6666666665 = 9.02465758 Simplifying x + -0.6666666665 = 9.02465758 Reorder the terms: -0.6666666665 + x = 9.02465758 Solving -0.6666666665 + x = 9.02465758 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 = 9.02465758 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 9.02465758 + 0.6666666665 x = 9.02465758 + 0.6666666665 Combine like terms: 9.02465758 + 0.6666666665 = 9.6913242465 x = 9.6913242465 Simplifying x = 9.6913242465Subproblem 2
x + -0.6666666665 = -9.02465758 Simplifying x + -0.6666666665 = -9.02465758 Reorder the terms: -0.6666666665 + x = -9.02465758 Solving -0.6666666665 + x = -9.02465758 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 = -9.02465758 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -9.02465758 + 0.6666666665 x = -9.02465758 + 0.6666666665 Combine like terms: -9.02465758 + 0.6666666665 = -8.3579909135 x = -8.3579909135 Simplifying x = -8.3579909135Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.6913242465, -8.3579909135}
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