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Simplifying 2x2 + 3x + -23 = 3 Reorder the terms: -23 + 3x + 2x2 = 3 Solving -23 + 3x + 2x2 = 3 Solving for variable 'x'. Reorder the terms: -23 + -3 + 3x + 2x2 = 3 + -3 Combine like terms: -23 + -3 = -26 -26 + 3x + 2x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -26 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13 + 1.5x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 1.5x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 1.5x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 1.5x + x2 = 0 + 13 1.5x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 1.5x + x2 = 13 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 = 13 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 13 + 0.5625 Combine like terms: 13 + 0.5625 = 13.5625 0.5625 + 1.5x + x2 = 13.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (x + 0.75) equal to 3.682729966 and -3.682729966.Subproblem 1
x + 0.75 = 3.682729966 Simplifying x + 0.75 = 3.682729966 Reorder the terms: 0.75 + x = 3.682729966 Solving 0.75 + x = 3.682729966 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 = 3.682729966 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 3.682729966 + -0.75 x = 3.682729966 + -0.75 Combine like terms: 3.682729966 + -0.75 = 2.932729966 x = 2.932729966 Simplifying x = 2.932729966Subproblem 2
x + 0.75 = -3.682729966 Simplifying x + 0.75 = -3.682729966 Reorder the terms: 0.75 + x = -3.682729966 Solving 0.75 + x = -3.682729966 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 = -3.682729966 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -3.682729966 + -0.75 x = -3.682729966 + -0.75 Combine like terms: -3.682729966 + -0.75 = -4.432729966 x = -4.432729966 Simplifying x = -4.432729966Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.932729966, -4.432729966}
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