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Simplifying 4x2 + 21x + 24 = 0 Reorder the terms: 24 + 21x + 4x2 = 0 Solving 24 + 21x + 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'. 6 + 5.25x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 5.25x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 5.25x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5.25x + x2 = 0 + -6 5.25x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 5.25x + x2 = -6 The x term is 5.25x. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25x + 6.890625 + x2 = -6 + 6.890625 Reorder the terms: 6.890625 + 5.25x + x2 = -6 + 6.890625 Combine like terms: -6 + 6.890625 = 0.890625 6.890625 + 5.25x + x2 = 0.890625 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (x + 2.625) equal to 0.943729304 and -0.943729304.Subproblem 1
x + 2.625 = 0.943729304 Simplifying x + 2.625 = 0.943729304 Reorder the terms: 2.625 + x = 0.943729304 Solving 2.625 + x = 0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = 0.943729304 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 0.943729304 + -2.625 x = 0.943729304 + -2.625 Combine like terms: 0.943729304 + -2.625 = -1.681270696 x = -1.681270696 Simplifying x = -1.681270696Subproblem 2
x + 2.625 = -0.943729304 Simplifying x + 2.625 = -0.943729304 Reorder the terms: 2.625 + x = -0.943729304 Solving 2.625 + x = -0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = -0.943729304 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -0.943729304 + -2.625 x = -0.943729304 + -2.625 Combine like terms: -0.943729304 + -2.625 = -3.568729304 x = -3.568729304 Simplifying x = -3.568729304Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.681270696, -3.568729304}
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