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Simplifying 2x2 + 18x = -7 Reorder the terms: 18x + 2x2 = -7 Solving 18x + 2x2 = -7 Solving for variable 'x'. Reorder the terms: 7 + 18x + 2x2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + 18x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + 9x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 9x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 9x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 9x + x2 = 0 + -3.5 9x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 9x + x2 = -3.5 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 = -3.5 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -3.5 + 20.25 Combine like terms: -3.5 + 20.25 = 16.75 20.25 + 9x + x2 = 16.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 16.75 Calculate the square root of the right side: 4.092676386 Break this problem into two subproblems by setting (x + 4.5) equal to 4.092676386 and -4.092676386.Subproblem 1
x + 4.5 = 4.092676386 Simplifying x + 4.5 = 4.092676386 Reorder the terms: 4.5 + x = 4.092676386 Solving 4.5 + x = 4.092676386 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 = 4.092676386 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.092676386 + -4.5 x = 4.092676386 + -4.5 Combine like terms: 4.092676386 + -4.5 = -0.407323614 x = -0.407323614 Simplifying x = -0.407323614Subproblem 2
x + 4.5 = -4.092676386 Simplifying x + 4.5 = -4.092676386 Reorder the terms: 4.5 + x = -4.092676386 Solving 4.5 + x = -4.092676386 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 = -4.092676386 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.092676386 + -4.5 x = -4.092676386 + -4.5 Combine like terms: -4.092676386 + -4.5 = -8.592676386 x = -8.592676386 Simplifying x = -8.592676386Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.407323614, -8.592676386}
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