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Simplifying 5 = -16x2 + 26x Reorder the terms: 5 = 26x + -16x2 Solving 5 = 26x + -16x2 Solving for variable 'x'. Reorder the terms: 5 + -26x + 16x2 = 26x + -26x + -16x2 + 16x2 Combine like terms: 26x + -26x = 0 5 + -26x + 16x2 = 0 + -16x2 + 16x2 5 + -26x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 5 + -26x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.3125 + -1.625x + x2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + -1.625x + -0.3125 + x2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + -1.625x + x2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + -1.625x + x2 = 0 + -0.3125 -1.625x + x2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 -1.625x + x2 = -0.3125 The x term is -1.625x. Take half its coefficient (-0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. -1.625x + 0.66015625 + x2 = -0.3125 + 0.66015625 Reorder the terms: 0.66015625 + -1.625x + x2 = -0.3125 + 0.66015625 Combine like terms: -0.3125 + 0.66015625 = 0.34765625 0.66015625 + -1.625x + x2 = 0.34765625 Factor a perfect square on the left side: (x + -0.8125)(x + -0.8125) = 0.34765625 Calculate the square root of the right side: 0.589623821 Break this problem into two subproblems by setting (x + -0.8125) equal to 0.589623821 and -0.589623821.Subproblem 1
x + -0.8125 = 0.589623821 Simplifying x + -0.8125 = 0.589623821 Reorder the terms: -0.8125 + x = 0.589623821 Solving -0.8125 + x = 0.589623821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + x = 0.589623821 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + x = 0.589623821 + 0.8125 x = 0.589623821 + 0.8125 Combine like terms: 0.589623821 + 0.8125 = 1.402123821 x = 1.402123821 Simplifying x = 1.402123821Subproblem 2
x + -0.8125 = -0.589623821 Simplifying x + -0.8125 = -0.589623821 Reorder the terms: -0.8125 + x = -0.589623821 Solving -0.8125 + x = -0.589623821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + x = -0.589623821 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + x = -0.589623821 + 0.8125 x = -0.589623821 + 0.8125 Combine like terms: -0.589623821 + 0.8125 = 0.222876179 x = 0.222876179 Simplifying x = 0.222876179Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.402123821, 0.222876179}
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