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Simplifying 2(8x2 + 3x) + -5(x + 1) = 0 Reorder the terms: 2(3x + 8x2) + -5(x + 1) = 0 (3x * 2 + 8x2 * 2) + -5(x + 1) = 0 (6x + 16x2) + -5(x + 1) = 0 Reorder the terms: 6x + 16x2 + -5(1 + x) = 0 6x + 16x2 + (1 * -5 + x * -5) = 0 6x + 16x2 + (-5 + -5x) = 0 Reorder the terms: -5 + 6x + -5x + 16x2 = 0 Combine like terms: 6x + -5x = 1x -5 + 1x + 16x2 = 0 Solving -5 + 1x + 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'. -0.3125 + 0.0625x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + 0.0625x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + 0.0625x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + 0.0625x + x2 = 0 + 0.3125 0.0625x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 0.0625x + x2 = 0.3125 The x term is 0.0625x. Take half its coefficient (0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. 0.0625x + 0.0009765625 + x2 = 0.3125 + 0.0009765625 Reorder the terms: 0.0009765625 + 0.0625x + x2 = 0.3125 + 0.0009765625 Combine like terms: 0.3125 + 0.0009765625 = 0.3134765625 0.0009765625 + 0.0625x + x2 = 0.3134765625 Factor a perfect square on the left side: (x + 0.03125)(x + 0.03125) = 0.3134765625 Calculate the square root of the right side: 0.559889777 Break this problem into two subproblems by setting (x + 0.03125) equal to 0.559889777 and -0.559889777.Subproblem 1
x + 0.03125 = 0.559889777 Simplifying x + 0.03125 = 0.559889777 Reorder the terms: 0.03125 + x = 0.559889777 Solving 0.03125 + x = 0.559889777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + x = 0.559889777 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + x = 0.559889777 + -0.03125 x = 0.559889777 + -0.03125 Combine like terms: 0.559889777 + -0.03125 = 0.528639777 x = 0.528639777 Simplifying x = 0.528639777Subproblem 2
x + 0.03125 = -0.559889777 Simplifying x + 0.03125 = -0.559889777 Reorder the terms: 0.03125 + x = -0.559889777 Solving 0.03125 + x = -0.559889777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + x = -0.559889777 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + x = -0.559889777 + -0.03125 x = -0.559889777 + -0.03125 Combine like terms: -0.559889777 + -0.03125 = -0.591139777 x = -0.591139777 Simplifying x = -0.591139777Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.528639777, -0.591139777}
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