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Simplifying 3x2 + 4x = 87 Reorder the terms: 4x + 3x2 = 87 Solving 4x + 3x2 = 87 Solving for variable 'x'. Reorder the terms: -87 + 4x + 3x2 = 87 + -87 Combine like terms: 87 + -87 = 0 -87 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -29 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '29' to each side of the equation. -29 + 1.333333333x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + 1.333333333x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 1.333333333x + x2 = 0 + 29 1.333333333x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 1.333333333x + x2 = 29 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 = 29 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 29 + 0.4444444442 Combine like terms: 29 + 0.4444444442 = 29.4444444442 0.4444444442 + 1.333333333x + x2 = 29.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 29.4444444442 Calculate the square root of the right side: 5.426273532 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 5.426273532 and -5.426273532.Subproblem 1
x + 0.6666666665 = 5.426273532 Simplifying x + 0.6666666665 = 5.426273532 Reorder the terms: 0.6666666665 + x = 5.426273532 Solving 0.6666666665 + x = 5.426273532 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 = 5.426273532 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 5.426273532 + -0.6666666665 x = 5.426273532 + -0.6666666665 Combine like terms: 5.426273532 + -0.6666666665 = 4.7596068655 x = 4.7596068655 Simplifying x = 4.7596068655Subproblem 2
x + 0.6666666665 = -5.426273532 Simplifying x + 0.6666666665 = -5.426273532 Reorder the terms: 0.6666666665 + x = -5.426273532 Solving 0.6666666665 + x = -5.426273532 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 = -5.426273532 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -5.426273532 + -0.6666666665 x = -5.426273532 + -0.6666666665 Combine like terms: -5.426273532 + -0.6666666665 = -6.0929401985 x = -6.0929401985 Simplifying x = -6.0929401985Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.7596068655, -6.0929401985}
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