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Simplifying 2x2 + 6x + -189 = 0 Reorder the terms: -189 + 6x + 2x2 = 0 Solving -189 + 6x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -94.5 + 3x + x2 = 0 Move the constant term to the right: Add '94.5' to each side of the equation. -94.5 + 3x + 94.5 + x2 = 0 + 94.5 Reorder the terms: -94.5 + 94.5 + 3x + x2 = 0 + 94.5 Combine like terms: -94.5 + 94.5 = 0.0 0.0 + 3x + x2 = 0 + 94.5 3x + x2 = 0 + 94.5 Combine like terms: 0 + 94.5 = 94.5 3x + x2 = 94.5 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 = 94.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 94.5 + 2.25 Combine like terms: 94.5 + 2.25 = 96.75 2.25 + 3x + x2 = 96.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 96.75 Calculate the square root of the right side: 9.836157786 Break this problem into two subproblems by setting (x + 1.5) equal to 9.836157786 and -9.836157786.Subproblem 1
x + 1.5 = 9.836157786 Simplifying x + 1.5 = 9.836157786 Reorder the terms: 1.5 + x = 9.836157786 Solving 1.5 + x = 9.836157786 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 = 9.836157786 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 9.836157786 + -1.5 x = 9.836157786 + -1.5 Combine like terms: 9.836157786 + -1.5 = 8.336157786 x = 8.336157786 Simplifying x = 8.336157786Subproblem 2
x + 1.5 = -9.836157786 Simplifying x + 1.5 = -9.836157786 Reorder the terms: 1.5 + x = -9.836157786 Solving 1.5 + x = -9.836157786 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 = -9.836157786 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -9.836157786 + -1.5 x = -9.836157786 + -1.5 Combine like terms: -9.836157786 + -1.5 = -11.336157786 x = -11.336157786 Simplifying x = -11.336157786Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.336157786, -11.336157786}
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