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Simplifying -27 = x2 + -16.8x Reorder the terms: -27 = -16.8x + x2 Solving -27 = -16.8x + x2 Solving for variable 'x'. Reorder the terms: -27 + 16.8x + -1x2 = -16.8x + 16.8x + x2 + -1x2 Combine like terms: -16.8x + 16.8x = 0.0 -27 + 16.8x + -1x2 = 0.0 + x2 + -1x2 -27 + 16.8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -27 + 16.8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 27 + -16.8x + x2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + -16.8x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -16.8x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -16.8x + x2 = 0 + -27 -16.8x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -16.8x + x2 = -27 The x term is -16.8x. Take half its coefficient (-8.4). Square it (70.56) and add it to both sides. Add '70.56' to each side of the equation. -16.8x + 70.56 + x2 = -27 + 70.56 Reorder the terms: 70.56 + -16.8x + x2 = -27 + 70.56 Combine like terms: -27 + 70.56 = 43.56 70.56 + -16.8x + x2 = 43.56 Factor a perfect square on the left side: (x + -8.4)(x + -8.4) = 43.56 Calculate the square root of the right side: 6.6 Break this problem into two subproblems by setting (x + -8.4) equal to 6.6 and -6.6.Subproblem 1
x + -8.4 = 6.6 Simplifying x + -8.4 = 6.6 Reorder the terms: -8.4 + x = 6.6 Solving -8.4 + x = 6.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.4' to each side of the equation. -8.4 + 8.4 + x = 6.6 + 8.4 Combine like terms: -8.4 + 8.4 = 0.0 0.0 + x = 6.6 + 8.4 x = 6.6 + 8.4 Combine like terms: 6.6 + 8.4 = 15 x = 15 Simplifying x = 15Subproblem 2
x + -8.4 = -6.6 Simplifying x + -8.4 = -6.6 Reorder the terms: -8.4 + x = -6.6 Solving -8.4 + x = -6.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.4' to each side of the equation. -8.4 + 8.4 + x = -6.6 + 8.4 Combine like terms: -8.4 + 8.4 = 0.0 0.0 + x = -6.6 + 8.4 x = -6.6 + 8.4 Combine like terms: -6.6 + 8.4 = 1.8 x = 1.8 Simplifying x = 1.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {15, 1.8}
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