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Simplifying 186 = 2x2 + 3x Reorder the terms: 186 = 3x + 2x2 Solving 186 = 3x + 2x2 Solving for variable 'x'. Reorder the terms: 186 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 186 + -3x + -2x2 = 0 + 2x2 + -2x2 186 + -3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 186 + -3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -93 + 1.5x + x2 = 0 Move the constant term to the right: Add '93' to each side of the equation. -93 + 1.5x + 93 + x2 = 0 + 93 Reorder the terms: -93 + 93 + 1.5x + x2 = 0 + 93 Combine like terms: -93 + 93 = 0 0 + 1.5x + x2 = 0 + 93 1.5x + x2 = 0 + 93 Combine like terms: 0 + 93 = 93 1.5x + x2 = 93 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 93 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 93 + 0.5625 Combine like terms: 93 + 0.5625 = 93.5625 0.5625 + 1.5x + x2 = 93.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 93.5625 Calculate the square root of the right side: 9.672771061 Break this problem into two subproblems by setting (x + 0.75) equal to 9.672771061 and -9.672771061.Subproblem 1
x + 0.75 = 9.672771061 Simplifying x + 0.75 = 9.672771061 Reorder the terms: 0.75 + x = 9.672771061 Solving 0.75 + x = 9.672771061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 9.672771061 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 9.672771061 + -0.75 x = 9.672771061 + -0.75 Combine like terms: 9.672771061 + -0.75 = 8.922771061 x = 8.922771061 Simplifying x = 8.922771061Subproblem 2
x + 0.75 = -9.672771061 Simplifying x + 0.75 = -9.672771061 Reorder the terms: 0.75 + x = -9.672771061 Solving 0.75 + x = -9.672771061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -9.672771061 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -9.672771061 + -0.75 x = -9.672771061 + -0.75 Combine like terms: -9.672771061 + -0.75 = -10.422771061 x = -10.422771061 Simplifying x = -10.422771061Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.922771061, -10.422771061}
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