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Simplifying x = -16x2 + 84x + 72 Reorder the terms: x = 72 + 84x + -16x2 Solving x = 72 + 84x + -16x2 Solving for variable 'x'. Reorder the terms: -72 + x + -84x + 16x2 = 72 + 84x + -16x2 + -72 + -84x + 16x2 Combine like terms: x + -84x = -83x -72 + -83x + 16x2 = 72 + 84x + -16x2 + -72 + -84x + 16x2 Reorder the terms: -72 + -83x + 16x2 = 72 + -72 + 84x + -84x + -16x2 + 16x2 Combine like terms: 72 + -72 = 0 -72 + -83x + 16x2 = 0 + 84x + -84x + -16x2 + 16x2 -72 + -83x + 16x2 = 84x + -84x + -16x2 + 16x2 Combine like terms: 84x + -84x = 0 -72 + -83x + 16x2 = 0 + -16x2 + 16x2 -72 + -83x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -72 + -83x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -4.5 + -5.1875x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -5.1875x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -5.1875x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -5.1875x + x2 = 0 + 4.5 -5.1875x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -5.1875x + x2 = 4.5 The x term is -5.1875x. Take half its coefficient (-2.59375). Square it (6.727539063) and add it to both sides. Add '6.727539063' to each side of the equation. -5.1875x + 6.727539063 + x2 = 4.5 + 6.727539063 Reorder the terms: 6.727539063 + -5.1875x + x2 = 4.5 + 6.727539063 Combine like terms: 4.5 + 6.727539063 = 11.227539063 6.727539063 + -5.1875x + x2 = 11.227539063 Factor a perfect square on the left side: (x + -2.59375)(x + -2.59375) = 11.227539063 Calculate the square root of the right side: 3.350752015 Break this problem into two subproblems by setting (x + -2.59375) equal to 3.350752015 and -3.350752015.Subproblem 1
x + -2.59375 = 3.350752015 Simplifying x + -2.59375 = 3.350752015 Reorder the terms: -2.59375 + x = 3.350752015 Solving -2.59375 + x = 3.350752015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.59375' to each side of the equation. -2.59375 + 2.59375 + x = 3.350752015 + 2.59375 Combine like terms: -2.59375 + 2.59375 = 0.00000 0.00000 + x = 3.350752015 + 2.59375 x = 3.350752015 + 2.59375 Combine like terms: 3.350752015 + 2.59375 = 5.944502015 x = 5.944502015 Simplifying x = 5.944502015Subproblem 2
x + -2.59375 = -3.350752015 Simplifying x + -2.59375 = -3.350752015 Reorder the terms: -2.59375 + x = -3.350752015 Solving -2.59375 + x = -3.350752015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.59375' to each side of the equation. -2.59375 + 2.59375 + x = -3.350752015 + 2.59375 Combine like terms: -2.59375 + 2.59375 = 0.00000 0.00000 + x = -3.350752015 + 2.59375 x = -3.350752015 + 2.59375 Combine like terms: -3.350752015 + 2.59375 = -0.757002015 x = -0.757002015 Simplifying x = -0.757002015Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.944502015, -0.757002015}
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