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Simplifying 30 = 4x + 3x2 Solving 30 = 4x + 3x2 Solving for variable 'x'. Reorder the terms: 30 + -4x + -3x2 = 4x + -4x + 3x2 + -3x2 Combine like terms: 4x + -4x = 0 30 + -4x + -3x2 = 0 + 3x2 + -3x2 30 + -4x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 30 + -4x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -10 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 1.333333333x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 1.333333333x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 1.333333333x + x2 = 0 + 10 1.333333333x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 1.333333333x + x2 = 10 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 = 10 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 10 + 0.4444444442 Combine like terms: 10 + 0.4444444442 = 10.4444444442 0.4444444442 + 1.333333333x + x2 = 10.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 10.4444444442 Calculate the square root of the right side: 3.231786572 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 3.231786572 and -3.231786572.Subproblem 1
x + 0.6666666665 = 3.231786572 Simplifying x + 0.6666666665 = 3.231786572 Reorder the terms: 0.6666666665 + x = 3.231786572 Solving 0.6666666665 + x = 3.231786572 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 = 3.231786572 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 3.231786572 + -0.6666666665 x = 3.231786572 + -0.6666666665 Combine like terms: 3.231786572 + -0.6666666665 = 2.5651199055 x = 2.5651199055 Simplifying x = 2.5651199055Subproblem 2
x + 0.6666666665 = -3.231786572 Simplifying x + 0.6666666665 = -3.231786572 Reorder the terms: 0.6666666665 + x = -3.231786572 Solving 0.6666666665 + x = -3.231786572 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 = -3.231786572 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -3.231786572 + -0.6666666665 x = -3.231786572 + -0.6666666665 Combine like terms: -3.231786572 + -0.6666666665 = -3.8984532385 x = -3.8984532385 Simplifying x = -3.8984532385Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5651199055, -3.8984532385}
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