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Simplifying 2x2 + -3x = 43 Reorder the terms: -3x + 2x2 = 43 Solving -3x + 2x2 = 43 Solving for variable 'x'. Reorder the terms: -43 + -3x + 2x2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -21.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '21.5' to each side of the equation. -21.5 + -1.5x + 21.5 + x2 = 0 + 21.5 Reorder the terms: -21.5 + 21.5 + -1.5x + x2 = 0 + 21.5 Combine like terms: -21.5 + 21.5 = 0.0 0.0 + -1.5x + x2 = 0 + 21.5 -1.5x + x2 = 0 + 21.5 Combine like terms: 0 + 21.5 = 21.5 -1.5x + x2 = 21.5 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 = 21.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 21.5 + 0.5625 Combine like terms: 21.5 + 0.5625 = 22.0625 0.5625 + -1.5x + x2 = 22.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 22.0625 Calculate the square root of the right side: 4.697073557 Break this problem into two subproblems by setting (x + -0.75) equal to 4.697073557 and -4.697073557.Subproblem 1
x + -0.75 = 4.697073557 Simplifying x + -0.75 = 4.697073557 Reorder the terms: -0.75 + x = 4.697073557 Solving -0.75 + x = 4.697073557 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 = 4.697073557 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 4.697073557 + 0.75 x = 4.697073557 + 0.75 Combine like terms: 4.697073557 + 0.75 = 5.447073557 x = 5.447073557 Simplifying x = 5.447073557Subproblem 2
x + -0.75 = -4.697073557 Simplifying x + -0.75 = -4.697073557 Reorder the terms: -0.75 + x = -4.697073557 Solving -0.75 + x = -4.697073557 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 = -4.697073557 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -4.697073557 + 0.75 x = -4.697073557 + 0.75 Combine like terms: -4.697073557 + 0.75 = -3.947073557 x = -3.947073557 Simplifying x = -3.947073557Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.447073557, -3.947073557}
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