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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 = 12.890625 6.890625 + 5.25x + x2 = 12.890625 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = 12.890625 Calculate the square root of the right side: 3.590351654 Break this problem into two subproblems by setting (x + 2.625) equal to 3.590351654 and -3.590351654.Subproblem 1
x + 2.625 = 3.590351654 Simplifying x + 2.625 = 3.590351654 Reorder the terms: 2.625 + x = 3.590351654 Solving 2.625 + x = 3.590351654 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 = 3.590351654 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 3.590351654 + -2.625 x = 3.590351654 + -2.625 Combine like terms: 3.590351654 + -2.625 = 0.965351654 x = 0.965351654 Simplifying x = 0.965351654Subproblem 2
x + 2.625 = -3.590351654 Simplifying x + 2.625 = -3.590351654 Reorder the terms: 2.625 + x = -3.590351654 Solving 2.625 + x = -3.590351654 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 = -3.590351654 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -3.590351654 + -2.625 x = -3.590351654 + -2.625 Combine like terms: -3.590351654 + -2.625 = -6.215351654 x = -6.215351654 Simplifying x = -6.215351654Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.965351654, -6.215351654}
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