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Simplifying -0.8x2 + 14.4x + 2 = 63.6 Reorder the terms: 2 + 14.4x + -0.8x2 = 63.6 Solving 2 + 14.4x + -0.8x2 = 63.6 Solving for variable 'x'. Reorder the terms: 2 + -63.6 + 14.4x + -0.8x2 = 63.6 + -63.6 Combine like terms: 2 + -63.6 = -61.6 -61.6 + 14.4x + -0.8x2 = 63.6 + -63.6 Combine like terms: 63.6 + -63.6 = 0.0 -61.6 + 14.4x + -0.8x2 = 0.0 Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. 77 + -18x + x2 = 0 Move the constant term to the right: Add '-77' to each side of the equation. 77 + -18x + -77 + x2 = 0 + -77 Reorder the terms: 77 + -77 + -18x + x2 = 0 + -77 Combine like terms: 77 + -77 = 0 0 + -18x + x2 = 0 + -77 -18x + x2 = 0 + -77 Combine like terms: 0 + -77 = -77 -18x + x2 = -77 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 = -77 + 81 Reorder the terms: 81 + -18x + x2 = -77 + 81 Combine like terms: -77 + 81 = 4 81 + -18x + x2 = 4 Factor a perfect square on the left side: (x + -9)(x + -9) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + -9) equal to 2 and -2.Subproblem 1
x + -9 = 2 Simplifying x + -9 = 2 Reorder the terms: -9 + x = 2 Solving -9 + x = 2 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 = 2 + 9 Combine like terms: -9 + 9 = 0 0 + x = 2 + 9 x = 2 + 9 Combine like terms: 2 + 9 = 11 x = 11 Simplifying x = 11Subproblem 2
x + -9 = -2 Simplifying x + -9 = -2 Reorder the terms: -9 + x = -2 Solving -9 + x = -2 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 = -2 + 9 Combine like terms: -9 + 9 = 0 0 + x = -2 + 9 x = -2 + 9 Combine like terms: -2 + 9 = 7 x = 7 Simplifying x = 7Solution
The solution to the problem is based on the solutions from the subproblems. x = {11, 7}
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