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Simplifying -1(16x2 + -89.6x + -90) = 0 Reorder the terms: -1(-90 + -89.6x + 16x2) = 0 (-90 * -1 + -89.6x * -1 + 16x2 * -1) = 0 (90 + 89.6x + -16x2) = 0 Solving 90 + 89.6x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -5.625 + -5.6x + x2 = 0 Move the constant term to the right: Add '5.625' to each side of the equation. -5.625 + -5.6x + 5.625 + x2 = 0 + 5.625 Reorder the terms: -5.625 + 5.625 + -5.6x + x2 = 0 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + -5.6x + x2 = 0 + 5.625 -5.6x + x2 = 0 + 5.625 Combine like terms: 0 + 5.625 = 5.625 -5.6x + x2 = 5.625 The x term is -5.6x. Take half its coefficient (-2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. -5.6x + 7.84 + x2 = 5.625 + 7.84 Reorder the terms: 7.84 + -5.6x + x2 = 5.625 + 7.84 Combine like terms: 5.625 + 7.84 = 13.465 7.84 + -5.6x + x2 = 13.465 Factor a perfect square on the left side: (x + -2.8)(x + -2.8) = 13.465 Calculate the square root of the right side: 3.669468626 Break this problem into two subproblems by setting (x + -2.8) equal to 3.669468626 and -3.669468626.Subproblem 1
x + -2.8 = 3.669468626 Simplifying x + -2.8 = 3.669468626 Reorder the terms: -2.8 + x = 3.669468626 Solving -2.8 + x = 3.669468626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = 3.669468626 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = 3.669468626 + 2.8 x = 3.669468626 + 2.8 Combine like terms: 3.669468626 + 2.8 = 6.469468626 x = 6.469468626 Simplifying x = 6.469468626Subproblem 2
x + -2.8 = -3.669468626 Simplifying x + -2.8 = -3.669468626 Reorder the terms: -2.8 + x = -3.669468626 Solving -2.8 + x = -3.669468626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = -3.669468626 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = -3.669468626 + 2.8 x = -3.669468626 + 2.8 Combine like terms: -3.669468626 + 2.8 = -0.869468626 x = -0.869468626 Simplifying x = -0.869468626Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.469468626, -0.869468626}
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