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Simplifying 9x2 + 14x + -16 = 0 Reorder the terms: -16 + 14x + 9x2 = 0 Solving -16 + 14x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.777777778 + 1.555555556x + x2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + 1.555555556x + 1.777777778 + x2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + 1.555555556x + x2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + 1.555555556x + x2 = 0 + 1.777777778 1.555555556x + x2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 1.555555556x + x2 = 1.777777778 The x term is 1.555555556x. Take half its coefficient (0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. 1.555555556x + 0.6049382720 + x2 = 1.777777778 + 0.6049382720 Reorder the terms: 0.6049382720 + 1.555555556x + x2 = 1.777777778 + 0.6049382720 Combine like terms: 1.777777778 + 0.6049382720 = 2.38271605 0.6049382720 + 1.555555556x + x2 = 2.38271605 Factor a perfect square on the left side: (x + 0.777777778)(x + 0.777777778) = 2.38271605 Calculate the square root of the right side: 1.543604888 Break this problem into two subproblems by setting (x + 0.777777778) equal to 1.543604888 and -1.543604888.Subproblem 1
x + 0.777777778 = 1.543604888 Simplifying x + 0.777777778 = 1.543604888 Reorder the terms: 0.777777778 + x = 1.543604888 Solving 0.777777778 + x = 1.543604888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = 1.543604888 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = 1.543604888 + -0.777777778 x = 1.543604888 + -0.777777778 Combine like terms: 1.543604888 + -0.777777778 = 0.76582711 x = 0.76582711 Simplifying x = 0.76582711Subproblem 2
x + 0.777777778 = -1.543604888 Simplifying x + 0.777777778 = -1.543604888 Reorder the terms: 0.777777778 + x = -1.543604888 Solving 0.777777778 + x = -1.543604888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = -1.543604888 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = -1.543604888 + -0.777777778 x = -1.543604888 + -0.777777778 Combine like terms: -1.543604888 + -0.777777778 = -2.321382666 x = -2.321382666 Simplifying x = -2.321382666Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.76582711, -2.321382666}
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