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Simplifying 2x(x + 9) = 153 Reorder the terms: 2x(9 + x) = 153 (9 * 2x + x * 2x) = 153 (18x + 2x2) = 153 Solving 18x + 2x2 = 153 Solving for variable 'x'. Reorder the terms: -153 + 18x + 2x2 = 153 + -153 Combine like terms: 153 + -153 = 0 -153 + 18x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -76.5 + 9x + x2 = 0 Move the constant term to the right: Add '76.5' to each side of the equation. -76.5 + 9x + 76.5 + x2 = 0 + 76.5 Reorder the terms: -76.5 + 76.5 + 9x + x2 = 0 + 76.5 Combine like terms: -76.5 + 76.5 = 0.0 0.0 + 9x + x2 = 0 + 76.5 9x + x2 = 0 + 76.5 Combine like terms: 0 + 76.5 = 76.5 9x + x2 = 76.5 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 76.5 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 76.5 + 20.25 Combine like terms: 76.5 + 20.25 = 96.75 20.25 + 9x + x2 = 96.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 96.75 Calculate the square root of the right side: 9.836157786 Break this problem into two subproblems by setting (x + 4.5) equal to 9.836157786 and -9.836157786.Subproblem 1
x + 4.5 = 9.836157786 Simplifying x + 4.5 = 9.836157786 Reorder the terms: 4.5 + x = 9.836157786 Solving 4.5 + x = 9.836157786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 9.836157786 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 9.836157786 + -4.5 x = 9.836157786 + -4.5 Combine like terms: 9.836157786 + -4.5 = 5.336157786 x = 5.336157786 Simplifying x = 5.336157786Subproblem 2
x + 4.5 = -9.836157786 Simplifying x + 4.5 = -9.836157786 Reorder the terms: 4.5 + x = -9.836157786 Solving 4.5 + x = -9.836157786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -9.836157786 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -9.836157786 + -4.5 x = -9.836157786 + -4.5 Combine like terms: -9.836157786 + -4.5 = -14.336157786 x = -14.336157786 Simplifying x = -14.336157786Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.336157786, -14.336157786}
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