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Simplifying 7x2 + -16x + 5 = 0 Reorder the terms: 5 + -16x + 7x2 = 0 Solving 5 + -16x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.7142857143 + -2.285714286x + x2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + -2.285714286x + -0.7142857143 + x2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + -2.285714286x + x2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + -2.285714286x + x2 = 0 + -0.7142857143 -2.285714286x + x2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 -2.285714286x + x2 = -0.7142857143 The x term is -2.285714286x. Take half its coefficient (-1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. -2.285714286x + 1.306122449 + x2 = -0.7142857143 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286x + x2 = -0.7142857143 + 1.306122449 Combine like terms: -0.7142857143 + 1.306122449 = 0.5918367347 1.306122449 + -2.285714286x + x2 = 0.5918367347 Factor a perfect square on the left side: (x + -1.142857143)(x + -1.142857143) = 0.5918367347 Calculate the square root of the right side: 0.769309258 Break this problem into two subproblems by setting (x + -1.142857143) equal to 0.769309258 and -0.769309258.Subproblem 1
x + -1.142857143 = 0.769309258 Simplifying x + -1.142857143 = 0.769309258 Reorder the terms: -1.142857143 + x = 0.769309258 Solving -1.142857143 + x = 0.769309258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + x = 0.769309258 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = 0.769309258 + 1.142857143 x = 0.769309258 + 1.142857143 Combine like terms: 0.769309258 + 1.142857143 = 1.912166401 x = 1.912166401 Simplifying x = 1.912166401Subproblem 2
x + -1.142857143 = -0.769309258 Simplifying x + -1.142857143 = -0.769309258 Reorder the terms: -1.142857143 + x = -0.769309258 Solving -1.142857143 + x = -0.769309258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + x = -0.769309258 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = -0.769309258 + 1.142857143 x = -0.769309258 + 1.142857143 Combine like terms: -0.769309258 + 1.142857143 = 0.373547885 x = 0.373547885 Simplifying x = 0.373547885Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.912166401, 0.373547885}
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