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Simplifying 18x + -9x2 + 169 = 0 Reorder the terms: 169 + 18x + -9x2 = 0 Solving 169 + 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'. -18.77777778 + -2x + x2 = 0 Move the constant term to the right: Add '18.77777778' to each side of the equation. -18.77777778 + -2x + 18.77777778 + x2 = 0 + 18.77777778 Reorder the terms: -18.77777778 + 18.77777778 + -2x + x2 = 0 + 18.77777778 Combine like terms: -18.77777778 + 18.77777778 = 0.00000000 0.00000000 + -2x + x2 = 0 + 18.77777778 -2x + x2 = 0 + 18.77777778 Combine like terms: 0 + 18.77777778 = 18.77777778 -2x + x2 = 18.77777778 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 = 18.77777778 + 1 Reorder the terms: 1 + -2x + x2 = 18.77777778 + 1 Combine like terms: 18.77777778 + 1 = 19.77777778 1 + -2x + x2 = 19.77777778 Factor a perfect square on the left side: (x + -1)(x + -1) = 19.77777778 Calculate the square root of the right side: 4.447221355 Break this problem into two subproblems by setting (x + -1) equal to 4.447221355 and -4.447221355.Subproblem 1
x + -1 = 4.447221355 Simplifying x + -1 = 4.447221355 Reorder the terms: -1 + x = 4.447221355 Solving -1 + x = 4.447221355 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 = 4.447221355 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.447221355 + 1 x = 4.447221355 + 1 Combine like terms: 4.447221355 + 1 = 5.447221355 x = 5.447221355 Simplifying x = 5.447221355Subproblem 2
x + -1 = -4.447221355 Simplifying x + -1 = -4.447221355 Reorder the terms: -1 + x = -4.447221355 Solving -1 + x = -4.447221355 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 = -4.447221355 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.447221355 + 1 x = -4.447221355 + 1 Combine like terms: -4.447221355 + 1 = -3.447221355 x = -3.447221355 Simplifying x = -3.447221355Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.447221355, -3.447221355}
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