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Simplifying 54x2 + -54x + -7.18 = 0 Reorder the terms: -7.18 + -54x + 54x2 = 0 Solving -7.18 + -54x + 54x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 54 the coefficient of the squared term: Divide each side by '54'. -0.132962963 + -1x + x2 = 0 Move the constant term to the right: Add '0.132962963' to each side of the equation. -0.132962963 + -1x + 0.132962963 + x2 = 0 + 0.132962963 Reorder the terms: -0.132962963 + 0.132962963 + -1x + x2 = 0 + 0.132962963 Combine like terms: -0.132962963 + 0.132962963 = 0.000000000 0.000000000 + -1x + x2 = 0 + 0.132962963 -1x + x2 = 0 + 0.132962963 Combine like terms: 0 + 0.132962963 = 0.132962963 -1x + x2 = 0.132962963 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.132962963 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.132962963 + 0.25 Combine like terms: 0.132962963 + 0.25 = 0.382962963 0.25 + -1x + x2 = 0.382962963 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.382962963 Calculate the square root of the right side: 0.618840014 Break this problem into two subproblems by setting (x + -0.5) equal to 0.618840014 and -0.618840014.Subproblem 1
x + -0.5 = 0.618840014 Simplifying x + -0.5 = 0.618840014 Reorder the terms: -0.5 + x = 0.618840014 Solving -0.5 + x = 0.618840014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.618840014 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.618840014 + 0.5 x = 0.618840014 + 0.5 Combine like terms: 0.618840014 + 0.5 = 1.118840014 x = 1.118840014 Simplifying x = 1.118840014Subproblem 2
x + -0.5 = -0.618840014 Simplifying x + -0.5 = -0.618840014 Reorder the terms: -0.5 + x = -0.618840014 Solving -0.5 + x = -0.618840014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.618840014 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.618840014 + 0.5 x = -0.618840014 + 0.5 Combine like terms: -0.618840014 + 0.5 = -0.118840014 x = -0.118840014 Simplifying x = -0.118840014Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.118840014, -0.118840014}
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