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Simplifying x(x + 1) = 15x + 80 Reorder the terms: x(1 + x) = 15x + 80 (1 * x + x * x) = 15x + 80 (1x + x2) = 15x + 80 Reorder the terms: 1x + x2 = 80 + 15x Solving 1x + x2 = 80 + 15x Solving for variable 'x'. Reorder the terms: -80 + 1x + -15x + x2 = 80 + 15x + -80 + -15x Combine like terms: 1x + -15x = -14x -80 + -14x + x2 = 80 + 15x + -80 + -15x Reorder the terms: -80 + -14x + x2 = 80 + -80 + 15x + -15x Combine like terms: 80 + -80 = 0 -80 + -14x + x2 = 0 + 15x + -15x -80 + -14x + x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -80 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -14x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + -14x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -14x + x2 = 0 + 80 -14x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 -14x + x2 = 80 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 80 + 49 Reorder the terms: 49 + -14x + x2 = 80 + 49 Combine like terms: 80 + 49 = 129 49 + -14x + x2 = 129 Factor a perfect square on the left side: (x + -7)(x + -7) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (x + -7) equal to 11.357816692 and -11.357816692.Subproblem 1
x + -7 = 11.357816692 Simplifying x + -7 = 11.357816692 Reorder the terms: -7 + x = 11.357816692 Solving -7 + x = 11.357816692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 11.357816692 + 7 Combine like terms: -7 + 7 = 0 0 + x = 11.357816692 + 7 x = 11.357816692 + 7 Combine like terms: 11.357816692 + 7 = 18.357816692 x = 18.357816692 Simplifying x = 18.357816692Subproblem 2
x + -7 = -11.357816692 Simplifying x + -7 = -11.357816692 Reorder the terms: -7 + x = -11.357816692 Solving -7 + x = -11.357816692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -11.357816692 + 7 Combine like terms: -7 + 7 = 0 0 + x = -11.357816692 + 7 x = -11.357816692 + 7 Combine like terms: -11.357816692 + 7 = -4.357816692 x = -4.357816692 Simplifying x = -4.357816692Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.357816692, -4.357816692}
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