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Simplifying 5 + 3x(4x + -6) = 0 Reorder the terms: 5 + 3x(-6 + 4x) = 0 5 + (-6 * 3x + 4x * 3x) = 0 5 + (-18x + 12x2) = 0 Solving 5 + -18x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.4166666667 + -1.5x + x2 = 0 Move the constant term to the right: Add '-0.4166666667' to each side of the equation. 0.4166666667 + -1.5x + -0.4166666667 + x2 = 0 + -0.4166666667 Reorder the terms: 0.4166666667 + -0.4166666667 + -1.5x + x2 = 0 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + -1.5x + x2 = 0 + -0.4166666667 -1.5x + x2 = 0 + -0.4166666667 Combine like terms: 0 + -0.4166666667 = -0.4166666667 -1.5x + x2 = -0.4166666667 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -0.4166666667 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -0.4166666667 + 0.5625 Combine like terms: -0.4166666667 + 0.5625 = 0.1458333333 0.5625 + -1.5x + x2 = 0.1458333333 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.1458333333 Calculate the square root of the right side: 0.381881308 Break this problem into two subproblems by setting (x + -0.75) equal to 0.381881308 and -0.381881308.Subproblem 1
x + -0.75 = 0.381881308 Simplifying x + -0.75 = 0.381881308 Reorder the terms: -0.75 + x = 0.381881308 Solving -0.75 + x = 0.381881308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.381881308 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.381881308 + 0.75 x = 0.381881308 + 0.75 Combine like terms: 0.381881308 + 0.75 = 1.131881308 x = 1.131881308 Simplifying x = 1.131881308Subproblem 2
x + -0.75 = -0.381881308 Simplifying x + -0.75 = -0.381881308 Reorder the terms: -0.75 + x = -0.381881308 Solving -0.75 + x = -0.381881308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.381881308 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.381881308 + 0.75 x = -0.381881308 + 0.75 Combine like terms: -0.381881308 + 0.75 = 0.368118692 x = 0.368118692 Simplifying x = 0.368118692Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.131881308, 0.368118692}
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