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Simplifying 0 = -1.6x2 + 10.5x + 5.7 Reorder the terms: 0 = 5.7 + 10.5x + -1.6x2 Solving 0 = 5.7 + 10.5x + -1.6x2 Solving for variable 'x'. Combine like terms: 0 + -5.7 = -5.7 -5.7 + -10.5x + 1.6x2 = 5.7 + 10.5x + -1.6x2 + -5.7 + -10.5x + 1.6x2 Reorder the terms: -5.7 + -10.5x + 1.6x2 = 5.7 + -5.7 + 10.5x + -10.5x + -1.6x2 + 1.6x2 Combine like terms: 5.7 + -5.7 = 0.0 -5.7 + -10.5x + 1.6x2 = 0.0 + 10.5x + -10.5x + -1.6x2 + 1.6x2 -5.7 + -10.5x + 1.6x2 = 10.5x + -10.5x + -1.6x2 + 1.6x2 Combine like terms: 10.5x + -10.5x = 0.0 -5.7 + -10.5x + 1.6x2 = 0.0 + -1.6x2 + 1.6x2 -5.7 + -10.5x + 1.6x2 = -1.6x2 + 1.6x2 Combine like terms: -1.6x2 + 1.6x2 = 0.0 -5.7 + -10.5x + 1.6x2 = 0.0 Begin completing the square. Divide all terms by 1.6 the coefficient of the squared term: Divide each side by '1.6'. -3.5625 + -6.5625x + x2 = 0 Move the constant term to the right: Add '3.5625' to each side of the equation. -3.5625 + -6.5625x + 3.5625 + x2 = 0 + 3.5625 Reorder the terms: -3.5625 + 3.5625 + -6.5625x + x2 = 0 + 3.5625 Combine like terms: -3.5625 + 3.5625 = 0.0000 0.0000 + -6.5625x + x2 = 0 + 3.5625 -6.5625x + x2 = 0 + 3.5625 Combine like terms: 0 + 3.5625 = 3.5625 -6.5625x + x2 = 3.5625 The x term is -6.5625x. Take half its coefficient (-3.28125). Square it (10.76660156) and add it to both sides. Add '10.76660156' to each side of the equation. -6.5625x + 10.76660156 + x2 = 3.5625 + 10.76660156 Reorder the terms: 10.76660156 + -6.5625x + x2 = 3.5625 + 10.76660156 Combine like terms: 3.5625 + 10.76660156 = 14.32910156 10.76660156 + -6.5625x + x2 = 14.32910156 Factor a perfect square on the left side: (x + -3.28125)(x + -3.28125) = 14.32910156 Calculate the square root of the right side: 3.785379976 Break this problem into two subproblems by setting (x + -3.28125) equal to 3.785379976 and -3.785379976.Subproblem 1
x + -3.28125 = 3.785379976 Simplifying x + -3.28125 = 3.785379976 Reorder the terms: -3.28125 + x = 3.785379976 Solving -3.28125 + x = 3.785379976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.28125' to each side of the equation. -3.28125 + 3.28125 + x = 3.785379976 + 3.28125 Combine like terms: -3.28125 + 3.28125 = 0.00000 0.00000 + x = 3.785379976 + 3.28125 x = 3.785379976 + 3.28125 Combine like terms: 3.785379976 + 3.28125 = 7.066629976 x = 7.066629976 Simplifying x = 7.066629976Subproblem 2
x + -3.28125 = -3.785379976 Simplifying x + -3.28125 = -3.785379976 Reorder the terms: -3.28125 + x = -3.785379976 Solving -3.28125 + x = -3.785379976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.28125' to each side of the equation. -3.28125 + 3.28125 + x = -3.785379976 + 3.28125 Combine like terms: -3.28125 + 3.28125 = 0.00000 0.00000 + x = -3.785379976 + 3.28125 x = -3.785379976 + 3.28125 Combine like terms: -3.785379976 + 3.28125 = -0.504129976 x = -0.504129976 Simplifying x = -0.504129976Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.066629976, -0.504129976}
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