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Simplifying 4x2 + 21x = -4 Reorder the terms: 21x + 4x2 = -4 Solving 21x + 4x2 = -4 Solving for variable 'x'. Reorder the terms: 4 + 21x + 4x2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + 21x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + 5.25x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 5.25x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 5.25x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5.25x + x2 = 0 + -1 5.25x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 5.25x + x2 = -1 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 = -1 + 6.890625 Reorder the terms: 6.890625 + 5.25x + x2 = -1 + 6.890625 Combine like terms: -1 + 6.890625 = 5.890625 6.890625 + 5.25x + x2 = 5.890625 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = 5.890625 Calculate the square root of the right side: 2.42706098 Break this problem into two subproblems by setting (x + 2.625) equal to 2.42706098 and -2.42706098.Subproblem 1
x + 2.625 = 2.42706098 Simplifying x + 2.625 = 2.42706098 Reorder the terms: 2.625 + x = 2.42706098 Solving 2.625 + x = 2.42706098 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 = 2.42706098 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 2.42706098 + -2.625 x = 2.42706098 + -2.625 Combine like terms: 2.42706098 + -2.625 = -0.19793902 x = -0.19793902 Simplifying x = -0.19793902Subproblem 2
x + 2.625 = -2.42706098 Simplifying x + 2.625 = -2.42706098 Reorder the terms: 2.625 + x = -2.42706098 Solving 2.625 + x = -2.42706098 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 = -2.42706098 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -2.42706098 + -2.625 x = -2.42706098 + -2.625 Combine like terms: -2.42706098 + -2.625 = -5.05206098 x = -5.05206098 Simplifying x = -5.05206098Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.19793902, -5.05206098}
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