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Simplifying 7x2 + 5x + -16 = 0 Reorder the terms: -16 + 5x + 7x2 = 0 Solving -16 + 5x + 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'. -2.285714286 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + 0.7142857143x + 2.285714286 + x2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + 0.7142857143x + x2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + 0.7142857143x + x2 = 0 + 2.285714286 0.7142857143x + x2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 0.7142857143x + x2 = 2.285714286 The x term is 0.7142857143x. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143x + 0.1275510204 + x2 = 2.285714286 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = 2.285714286 + 0.1275510204 Combine like terms: 2.285714286 + 0.1275510204 = 2.4132653064 0.1275510204 + 0.7142857143x + x2 = 2.4132653064 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = 2.4132653064 Calculate the square root of the right side: 1.553468798 Break this problem into two subproblems by setting (x + 0.3571428572) equal to 1.553468798 and -1.553468798.Subproblem 1
x + 0.3571428572 = 1.553468798 Simplifying x + 0.3571428572 = 1.553468798 Reorder the terms: 0.3571428572 + x = 1.553468798 Solving 0.3571428572 + x = 1.553468798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = 1.553468798 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 1.553468798 + -0.3571428572 x = 1.553468798 + -0.3571428572 Combine like terms: 1.553468798 + -0.3571428572 = 1.1963259408 x = 1.1963259408 Simplifying x = 1.1963259408Subproblem 2
x + 0.3571428572 = -1.553468798 Simplifying x + 0.3571428572 = -1.553468798 Reorder the terms: 0.3571428572 + x = -1.553468798 Solving 0.3571428572 + x = -1.553468798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = -1.553468798 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -1.553468798 + -0.3571428572 x = -1.553468798 + -0.3571428572 Combine like terms: -1.553468798 + -0.3571428572 = -1.9106116552 x = -1.9106116552 Simplifying x = -1.9106116552Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1963259408, -1.9106116552}
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