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Simplifying x = 9x2 + -16 Reorder the terms: x = -16 + 9x2 Solving x = -16 + 9x2 Solving for variable 'x'. Reorder the terms: 16 + x + -9x2 = -16 + 9x2 + 16 + -9x2 Reorder the terms: 16 + x + -9x2 = -16 + 16 + 9x2 + -9x2 Combine like terms: -16 + 16 = 0 16 + x + -9x2 = 0 + 9x2 + -9x2 16 + x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 16 + x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -1.777777778 + -0.1111111111x + x2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + -0.1111111111x + 1.777777778 + x2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + -0.1111111111x + x2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + -0.1111111111x + x2 = 0 + 1.777777778 -0.1111111111x + x2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 -0.1111111111x + x2 = 1.777777778 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.1111111111x + 0.25 + x2 = 1.777777778 + 0.25 Reorder the terms: 0.25 + -0.1111111111x + x2 = 1.777777778 + 0.25 Combine like terms: 1.777777778 + 0.25 = 2.027777778 0.25 + -0.1111111111x + x2 = 2.027777778 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.027777778 Calculate the square root of the right side: 1.424000624 Break this problem into two subproblems by setting (x + 0.5) equal to 1.424000624 and -1.424000624.Subproblem 1
x + 0.5 = 1.424000624 Simplifying x + 0.5 = 1.424000624 Reorder the terms: 0.5 + x = 1.424000624 Solving 0.5 + x = 1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.424000624 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.424000624 + -0.5 x = 1.424000624 + -0.5 Combine like terms: 1.424000624 + -0.5 = 0.924000624 x = 0.924000624 Simplifying x = 0.924000624Subproblem 2
x + 0.5 = -1.424000624 Simplifying x + 0.5 = -1.424000624 Reorder the terms: 0.5 + x = -1.424000624 Solving 0.5 + x = -1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.424000624 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.424000624 + -0.5 x = -1.424000624 + -0.5 Combine like terms: -1.424000624 + -0.5 = -1.924000624 x = -1.924000624 Simplifying x = -1.924000624Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.924000624, -1.924000624}
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