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Simplifying 4x2 + 23x = -24 Reorder the terms: 23x + 4x2 = -24 Solving 23x + 4x2 = -24 Solving for variable 'x'. Reorder the terms: 24 + 23x + 4x2 = -24 + 24 Combine like terms: -24 + 24 = 0 24 + 23x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6 + 5.75x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 5.75x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 5.75x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5.75x + x2 = 0 + -6 5.75x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 5.75x + x2 = -6 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 = -6 + 8.265625 Reorder the terms: 8.265625 + 5.75x + x2 = -6 + 8.265625 Combine like terms: -6 + 8.265625 = 2.265625 8.265625 + 5.75x + x2 = 2.265625 Factor a perfect square on the left side: (x + 2.875)(x + 2.875) = 2.265625 Calculate the square root of the right side: 1.505199322 Break this problem into two subproblems by setting (x + 2.875) equal to 1.505199322 and -1.505199322.Subproblem 1
x + 2.875 = 1.505199322 Simplifying x + 2.875 = 1.505199322 Reorder the terms: 2.875 + x = 1.505199322 Solving 2.875 + x = 1.505199322 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 = 1.505199322 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = 1.505199322 + -2.875 x = 1.505199322 + -2.875 Combine like terms: 1.505199322 + -2.875 = -1.369800678 x = -1.369800678 Simplifying x = -1.369800678Subproblem 2
x + 2.875 = -1.505199322 Simplifying x + 2.875 = -1.505199322 Reorder the terms: 2.875 + x = -1.505199322 Solving 2.875 + x = -1.505199322 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 = -1.505199322 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = -1.505199322 + -2.875 x = -1.505199322 + -2.875 Combine like terms: -1.505199322 + -2.875 = -4.380199322 x = -4.380199322 Simplifying x = -4.380199322Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.369800678, -4.380199322}
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