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Simplifying -3x2 + 54x = 13 Reorder the terms: 54x + -3x2 = 13 Solving 54x + -3x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + 54x + -3x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 54x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 4.333333333 + -18x + x2 = 0 Move the constant term to the right: Add '-4.333333333' to each side of the equation. 4.333333333 + -18x + -4.333333333 + x2 = 0 + -4.333333333 Reorder the terms: 4.333333333 + -4.333333333 + -18x + x2 = 0 + -4.333333333 Combine like terms: 4.333333333 + -4.333333333 = 0.000000000 0.000000000 + -18x + x2 = 0 + -4.333333333 -18x + x2 = 0 + -4.333333333 Combine like terms: 0 + -4.333333333 = -4.333333333 -18x + x2 = -4.333333333 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -4.333333333 + 81 Reorder the terms: 81 + -18x + x2 = -4.333333333 + 81 Combine like terms: -4.333333333 + 81 = 76.666666667 81 + -18x + x2 = 76.666666667 Factor a perfect square on the left side: (x + -9)(x + -9) = 76.666666667 Calculate the square root of the right side: 8.755950358 Break this problem into two subproblems by setting (x + -9) equal to 8.755950358 and -8.755950358.Subproblem 1
x + -9 = 8.755950358 Simplifying x + -9 = 8.755950358 Reorder the terms: -9 + x = 8.755950358 Solving -9 + x = 8.755950358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 8.755950358 + 9 Combine like terms: -9 + 9 = 0 0 + x = 8.755950358 + 9 x = 8.755950358 + 9 Combine like terms: 8.755950358 + 9 = 17.755950358 x = 17.755950358 Simplifying x = 17.755950358Subproblem 2
x + -9 = -8.755950358 Simplifying x + -9 = -8.755950358 Reorder the terms: -9 + x = -8.755950358 Solving -9 + x = -8.755950358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -8.755950358 + 9 Combine like terms: -9 + 9 = 0 0 + x = -8.755950358 + 9 x = -8.755950358 + 9 Combine like terms: -8.755950358 + 9 = 0.244049642 x = 0.244049642 Simplifying x = 0.244049642Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.755950358, 0.244049642}
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