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Simplifying 84 = (x + 3)(x) Reorder the terms: 84 = (3 + x)(x) Reorder the terms for easier multiplication: 84 = x(3 + x) 84 = (3 * x + x * x) 84 = (3x + x2) Solving 84 = 3x + x2 Solving for variable 'x'. Reorder the terms: 84 + -3x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 84 + -3x + -1x2 = 0 + x2 + -1x2 84 + -3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 84 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -84 + 3x + x2 = 0 Move the constant term to the right: Add '84' to each side of the equation. -84 + 3x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + 3x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 3x + x2 = 0 + 84 3x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 3x + x2 = 84 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 84 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 84 + 2.25 Combine like terms: 84 + 2.25 = 86.25 2.25 + 3x + x2 = 86.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 86.25 Calculate the square root of the right side: 9.287087811 Break this problem into two subproblems by setting (x + 1.5) equal to 9.287087811 and -9.287087811.Subproblem 1
x + 1.5 = 9.287087811 Simplifying x + 1.5 = 9.287087811 Reorder the terms: 1.5 + x = 9.287087811 Solving 1.5 + x = 9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 9.287087811 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 9.287087811 + -1.5 x = 9.287087811 + -1.5 Combine like terms: 9.287087811 + -1.5 = 7.787087811 x = 7.787087811 Simplifying x = 7.787087811Subproblem 2
x + 1.5 = -9.287087811 Simplifying x + 1.5 = -9.287087811 Reorder the terms: 1.5 + x = -9.287087811 Solving 1.5 + x = -9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -9.287087811 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -9.287087811 + -1.5 x = -9.287087811 + -1.5 Combine like terms: -9.287087811 + -1.5 = -10.787087811 x = -10.787087811 Simplifying x = -10.787087811Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.787087811, -10.787087811}
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