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Simplifying 2x2 + 3x + -330 = 0 Reorder the terms: -330 + 3x + 2x2 = 0 Solving -330 + 3x + 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'. -165 + 1.5x + x2 = 0 Move the constant term to the right: Add '165' to each side of the equation. -165 + 1.5x + 165 + x2 = 0 + 165 Reorder the terms: -165 + 165 + 1.5x + x2 = 0 + 165 Combine like terms: -165 + 165 = 0 0 + 1.5x + x2 = 0 + 165 1.5x + x2 = 0 + 165 Combine like terms: 0 + 165 = 165 1.5x + x2 = 165 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 = 165 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 165 + 0.5625 Combine like terms: 165 + 0.5625 = 165.5625 0.5625 + 1.5x + x2 = 165.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 165.5625 Calculate the square root of the right side: 12.867109232 Break this problem into two subproblems by setting (x + 0.75) equal to 12.867109232 and -12.867109232.Subproblem 1
x + 0.75 = 12.867109232 Simplifying x + 0.75 = 12.867109232 Reorder the terms: 0.75 + x = 12.867109232 Solving 0.75 + x = 12.867109232 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 = 12.867109232 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 12.867109232 + -0.75 x = 12.867109232 + -0.75 Combine like terms: 12.867109232 + -0.75 = 12.117109232 x = 12.117109232 Simplifying x = 12.117109232Subproblem 2
x + 0.75 = -12.867109232 Simplifying x + 0.75 = -12.867109232 Reorder the terms: 0.75 + x = -12.867109232 Solving 0.75 + x = -12.867109232 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 = -12.867109232 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -12.867109232 + -0.75 x = -12.867109232 + -0.75 Combine like terms: -12.867109232 + -0.75 = -13.617109232 x = -13.617109232 Simplifying x = -13.617109232Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.117109232, -13.617109232}
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