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Simplifying 4x2 + -69x + 54 = 0 Reorder the terms: 54 + -69x + 4x2 = 0 Solving 54 + -69x + 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'. 13.5 + -17.25x + x2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + -17.25x + -13.5 + x2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + -17.25x + x2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + -17.25x + x2 = 0 + -13.5 -17.25x + x2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 -17.25x + x2 = -13.5 The x term is -17.25x. Take half its coefficient (-8.625). Square it (74.390625) and add it to both sides. Add '74.390625' to each side of the equation. -17.25x + 74.390625 + x2 = -13.5 + 74.390625 Reorder the terms: 74.390625 + -17.25x + x2 = -13.5 + 74.390625 Combine like terms: -13.5 + 74.390625 = 60.890625 74.390625 + -17.25x + x2 = 60.890625 Factor a perfect square on the left side: (x + -8.625)(x + -8.625) = 60.890625 Calculate the square root of the right side: 7.803244518 Break this problem into two subproblems by setting (x + -8.625) equal to 7.803244518 and -7.803244518.Subproblem 1
x + -8.625 = 7.803244518 Simplifying x + -8.625 = 7.803244518 Reorder the terms: -8.625 + x = 7.803244518 Solving -8.625 + x = 7.803244518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.625' to each side of the equation. -8.625 + 8.625 + x = 7.803244518 + 8.625 Combine like terms: -8.625 + 8.625 = 0.000 0.000 + x = 7.803244518 + 8.625 x = 7.803244518 + 8.625 Combine like terms: 7.803244518 + 8.625 = 16.428244518 x = 16.428244518 Simplifying x = 16.428244518Subproblem 2
x + -8.625 = -7.803244518 Simplifying x + -8.625 = -7.803244518 Reorder the terms: -8.625 + x = -7.803244518 Solving -8.625 + x = -7.803244518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.625' to each side of the equation. -8.625 + 8.625 + x = -7.803244518 + 8.625 Combine like terms: -8.625 + 8.625 = 0.000 0.000 + x = -7.803244518 + 8.625 x = -7.803244518 + 8.625 Combine like terms: -7.803244518 + 8.625 = 0.821755482 x = 0.821755482 Simplifying x = 0.821755482Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.428244518, 0.821755482}
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