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Simplifying 184 + 16x = (5x)(x + 1) Remove parenthesis around (5x) 184 + 16x = 5x(x + 1) Reorder the terms: 184 + 16x = 5x(1 + x) 184 + 16x = (1 * 5x + x * 5x) 184 + 16x = (5x + 5x2) Solving 184 + 16x = 5x + 5x2 Solving for variable 'x'. Combine like terms: 16x + -5x = 11x 184 + 11x + -5x2 = 5x + 5x2 + -5x + -5x2 Reorder the terms: 184 + 11x + -5x2 = 5x + -5x + 5x2 + -5x2 Combine like terms: 5x + -5x = 0 184 + 11x + -5x2 = 0 + 5x2 + -5x2 184 + 11x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 184 + 11x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -36.8 + -2.2x + x2 = 0 Move the constant term to the right: Add '36.8' to each side of the equation. -36.8 + -2.2x + 36.8 + x2 = 0 + 36.8 Reorder the terms: -36.8 + 36.8 + -2.2x + x2 = 0 + 36.8 Combine like terms: -36.8 + 36.8 = 0.0 0.0 + -2.2x + x2 = 0 + 36.8 -2.2x + x2 = 0 + 36.8 Combine like terms: 0 + 36.8 = 36.8 -2.2x + x2 = 36.8 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = 36.8 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = 36.8 + 1.21 Combine like terms: 36.8 + 1.21 = 38.01 1.21 + -2.2x + x2 = 38.01 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 38.01 Calculate the square root of the right side: 6.165225057 Break this problem into two subproblems by setting (x + -1.1) equal to 6.165225057 and -6.165225057.Subproblem 1
x + -1.1 = 6.165225057 Simplifying x + -1.1 = 6.165225057 Reorder the terms: -1.1 + x = 6.165225057 Solving -1.1 + x = 6.165225057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 6.165225057 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 6.165225057 + 1.1 x = 6.165225057 + 1.1 Combine like terms: 6.165225057 + 1.1 = 7.265225057 x = 7.265225057 Simplifying x = 7.265225057Subproblem 2
x + -1.1 = -6.165225057 Simplifying x + -1.1 = -6.165225057 Reorder the terms: -1.1 + x = -6.165225057 Solving -1.1 + x = -6.165225057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -6.165225057 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -6.165225057 + 1.1 x = -6.165225057 + 1.1 Combine like terms: -6.165225057 + 1.1 = -5.065225057 x = -5.065225057 Simplifying x = -5.065225057Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.265225057, -5.065225057}
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