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Simplifying 186 = 2x2 + 9x Reorder the terms: 186 = 9x + 2x2 Solving 186 = 9x + 2x2 Solving for variable 'x'. Reorder the terms: 186 + -9x + -2x2 = 9x + -9x + 2x2 + -2x2 Combine like terms: 9x + -9x = 0 186 + -9x + -2x2 = 0 + 2x2 + -2x2 186 + -9x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 186 + -9x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -93 + 4.5x + x2 = 0 Move the constant term to the right: Add '93' to each side of the equation. -93 + 4.5x + 93 + x2 = 0 + 93 Reorder the terms: -93 + 93 + 4.5x + x2 = 0 + 93 Combine like terms: -93 + 93 = 0 0 + 4.5x + x2 = 0 + 93 4.5x + x2 = 0 + 93 Combine like terms: 0 + 93 = 93 4.5x + x2 = 93 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 93 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 93 + 5.0625 Combine like terms: 93 + 5.0625 = 98.0625 5.0625 + 4.5x + x2 = 98.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 98.0625 Calculate the square root of the right side: 9.90265116 Break this problem into two subproblems by setting (x + 2.25) equal to 9.90265116 and -9.90265116.Subproblem 1
x + 2.25 = 9.90265116 Simplifying x + 2.25 = 9.90265116 Reorder the terms: 2.25 + x = 9.90265116 Solving 2.25 + x = 9.90265116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 9.90265116 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 9.90265116 + -2.25 x = 9.90265116 + -2.25 Combine like terms: 9.90265116 + -2.25 = 7.65265116 x = 7.65265116 Simplifying x = 7.65265116Subproblem 2
x + 2.25 = -9.90265116 Simplifying x + 2.25 = -9.90265116 Reorder the terms: 2.25 + x = -9.90265116 Solving 2.25 + x = -9.90265116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -9.90265116 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -9.90265116 + -2.25 x = -9.90265116 + -2.25 Combine like terms: -9.90265116 + -2.25 = -12.15265116 x = -12.15265116 Simplifying x = -12.15265116Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.65265116, -12.15265116}
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