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Simplifying 8x2 + -16x + 7 = 0 Reorder the terms: 7 + -16x + 8x2 = 0 Solving 7 + -16x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.875 + -2x + x2 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + -2x + -0.875 + x2 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + -2x + x2 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + -2x + x2 = 0 + -0.875 -2x + x2 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 -2x + x2 = -0.875 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.875 + 1 Reorder the terms: 1 + -2x + x2 = -0.875 + 1 Combine like terms: -0.875 + 1 = 0.125 1 + -2x + x2 = 0.125 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.125 Calculate the square root of the right side: 0.353553391 Break this problem into two subproblems by setting (x + -1) equal to 0.353553391 and -0.353553391.Subproblem 1
x + -1 = 0.353553391 Simplifying x + -1 = 0.353553391 Reorder the terms: -1 + x = 0.353553391 Solving -1 + x = 0.353553391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.353553391 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.353553391 + 1 x = 0.353553391 + 1 Combine like terms: 0.353553391 + 1 = 1.353553391 x = 1.353553391 Simplifying x = 1.353553391Subproblem 2
x + -1 = -0.353553391 Simplifying x + -1 = -0.353553391 Reorder the terms: -1 + x = -0.353553391 Solving -1 + x = -0.353553391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.353553391 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.353553391 + 1 x = -0.353553391 + 1 Combine like terms: -0.353553391 + 1 = 0.646446609 x = 0.646446609 Simplifying x = 0.646446609Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.353553391, 0.646446609}
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