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Simplifying 4x2 + 23x + -12 = 0 Reorder the terms: -12 + 23x + 4x2 = 0 Solving -12 + 23x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3 + 5.75x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 5.75x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 5.75x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 5.75x + x2 = 0 + 3 5.75x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 5.75x + x2 = 3 The x term is 5.75x. Take half its coefficient (2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. 5.75x + 8.265625 + x2 = 3 + 8.265625 Reorder the terms: 8.265625 + 5.75x + x2 = 3 + 8.265625 Combine like terms: 3 + 8.265625 = 11.265625 8.265625 + 5.75x + x2 = 11.265625 Factor a perfect square on the left side: (x + 2.875)(x + 2.875) = 11.265625 Calculate the square root of the right side: 3.356430396 Break this problem into two subproblems by setting (x + 2.875) equal to 3.356430396 and -3.356430396.Subproblem 1
x + 2.875 = 3.356430396 Simplifying x + 2.875 = 3.356430396 Reorder the terms: 2.875 + x = 3.356430396 Solving 2.875 + x = 3.356430396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = 3.356430396 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = 3.356430396 + -2.875 x = 3.356430396 + -2.875 Combine like terms: 3.356430396 + -2.875 = 0.481430396 x = 0.481430396 Simplifying x = 0.481430396Subproblem 2
x + 2.875 = -3.356430396 Simplifying x + 2.875 = -3.356430396 Reorder the terms: 2.875 + x = -3.356430396 Solving 2.875 + x = -3.356430396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = -3.356430396 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = -3.356430396 + -2.875 x = -3.356430396 + -2.875 Combine like terms: -3.356430396 + -2.875 = -6.231430396 x = -6.231430396 Simplifying x = -6.231430396Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.481430396, -6.231430396}
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