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Simplifying 4x2 + 53x = 53 Reorder the terms: 53x + 4x2 = 53 Solving 53x + 4x2 = 53 Solving for variable 'x'. Reorder the terms: -53 + 53x + 4x2 = 53 + -53 Combine like terms: 53 + -53 = 0 -53 + 53x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -13.25 + 13.25x + x2 = 0 Move the constant term to the right: Add '13.25' to each side of the equation. -13.25 + 13.25x + 13.25 + x2 = 0 + 13.25 Reorder the terms: -13.25 + 13.25 + 13.25x + x2 = 0 + 13.25 Combine like terms: -13.25 + 13.25 = 0.00 0.00 + 13.25x + x2 = 0 + 13.25 13.25x + x2 = 0 + 13.25 Combine like terms: 0 + 13.25 = 13.25 13.25x + x2 = 13.25 The x term is 13.25x. Take half its coefficient (6.625). Square it (43.890625) and add it to both sides. Add '43.890625' to each side of the equation. 13.25x + 43.890625 + x2 = 13.25 + 43.890625 Reorder the terms: 43.890625 + 13.25x + x2 = 13.25 + 43.890625 Combine like terms: 13.25 + 43.890625 = 57.140625 43.890625 + 13.25x + x2 = 57.140625 Factor a perfect square on the left side: (x + 6.625)(x + 6.625) = 57.140625 Calculate the square root of the right side: 7.559141816 Break this problem into two subproblems by setting (x + 6.625) equal to 7.559141816 and -7.559141816.Subproblem 1
x + 6.625 = 7.559141816 Simplifying x + 6.625 = 7.559141816 Reorder the terms: 6.625 + x = 7.559141816 Solving 6.625 + x = 7.559141816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.625' to each side of the equation. 6.625 + -6.625 + x = 7.559141816 + -6.625 Combine like terms: 6.625 + -6.625 = 0.000 0.000 + x = 7.559141816 + -6.625 x = 7.559141816 + -6.625 Combine like terms: 7.559141816 + -6.625 = 0.934141816 x = 0.934141816 Simplifying x = 0.934141816Subproblem 2
x + 6.625 = -7.559141816 Simplifying x + 6.625 = -7.559141816 Reorder the terms: 6.625 + x = -7.559141816 Solving 6.625 + x = -7.559141816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.625' to each side of the equation. 6.625 + -6.625 + x = -7.559141816 + -6.625 Combine like terms: 6.625 + -6.625 = 0.000 0.000 + x = -7.559141816 + -6.625 x = -7.559141816 + -6.625 Combine like terms: -7.559141816 + -6.625 = -14.184141816 x = -14.184141816 Simplifying x = -14.184141816Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.934141816, -14.184141816}
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