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Simplifying 2x2 + -3x + -459 = 0 Reorder the terms: -459 + -3x + 2x2 = 0 Solving -459 + -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'. -229.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '229.5' to each side of the equation. -229.5 + -1.5x + 229.5 + x2 = 0 + 229.5 Reorder the terms: -229.5 + 229.5 + -1.5x + x2 = 0 + 229.5 Combine like terms: -229.5 + 229.5 = 0.0 0.0 + -1.5x + x2 = 0 + 229.5 -1.5x + x2 = 0 + 229.5 Combine like terms: 0 + 229.5 = 229.5 -1.5x + x2 = 229.5 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 = 229.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 229.5 + 0.5625 Combine like terms: 229.5 + 0.5625 = 230.0625 0.5625 + -1.5x + x2 = 230.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 230.0625 Calculate the square root of the right side: 15.167811312 Break this problem into two subproblems by setting (x + -0.75) equal to 15.167811312 and -15.167811312.Subproblem 1
x + -0.75 = 15.167811312 Simplifying x + -0.75 = 15.167811312 Reorder the terms: -0.75 + x = 15.167811312 Solving -0.75 + x = 15.167811312 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 = 15.167811312 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 15.167811312 + 0.75 x = 15.167811312 + 0.75 Combine like terms: 15.167811312 + 0.75 = 15.917811312 x = 15.917811312 Simplifying x = 15.917811312Subproblem 2
x + -0.75 = -15.167811312 Simplifying x + -0.75 = -15.167811312 Reorder the terms: -0.75 + x = -15.167811312 Solving -0.75 + x = -15.167811312 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 = -15.167811312 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -15.167811312 + 0.75 x = -15.167811312 + 0.75 Combine like terms: -15.167811312 + 0.75 = -14.417811312 x = -14.417811312 Simplifying x = -14.417811312Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.917811312, -14.417811312}
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