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Simplifying 9x2 + -18x + -76 = 0 Reorder the terms: -76 + -18x + 9x2 = 0 Solving -76 + -18x + 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'. -8.444444444 + -2x + x2 = 0 Move the constant term to the right: Add '8.444444444' to each side of the equation. -8.444444444 + -2x + 8.444444444 + x2 = 0 + 8.444444444 Reorder the terms: -8.444444444 + 8.444444444 + -2x + x2 = 0 + 8.444444444 Combine like terms: -8.444444444 + 8.444444444 = 0.000000000 0.000000000 + -2x + x2 = 0 + 8.444444444 -2x + x2 = 0 + 8.444444444 Combine like terms: 0 + 8.444444444 = 8.444444444 -2x + x2 = 8.444444444 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 = 8.444444444 + 1 Reorder the terms: 1 + -2x + x2 = 8.444444444 + 1 Combine like terms: 8.444444444 + 1 = 9.444444444 1 + -2x + x2 = 9.444444444 Factor a perfect square on the left side: (x + -1)(x + -1) = 9.444444444 Calculate the square root of the right side: 3.073181486 Break this problem into two subproblems by setting (x + -1) equal to 3.073181486 and -3.073181486.Subproblem 1
x + -1 = 3.073181486 Simplifying x + -1 = 3.073181486 Reorder the terms: -1 + x = 3.073181486 Solving -1 + x = 3.073181486 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 = 3.073181486 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.073181486 + 1 x = 3.073181486 + 1 Combine like terms: 3.073181486 + 1 = 4.073181486 x = 4.073181486 Simplifying x = 4.073181486Subproblem 2
x + -1 = -3.073181486 Simplifying x + -1 = -3.073181486 Reorder the terms: -1 + x = -3.073181486 Solving -1 + x = -3.073181486 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 = -3.073181486 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.073181486 + 1 x = -3.073181486 + 1 Combine like terms: -3.073181486 + 1 = -2.073181486 x = -2.073181486 Simplifying x = -2.073181486Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.073181486, -2.073181486}
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