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Simplifying 9(x) = x2 + -1x + 4 + -9x Reorder the terms: 9x = 4 + -1x + -9x + x2 Combine like terms: -1x + -9x = -10x 9x = 4 + -10x + x2 Solving 9x = 4 + -10x + x2 Solving for variable 'x'. Reorder the terms: -4 + 9x + 10x + -1x2 = 4 + -10x + x2 + -4 + 10x + -1x2 Combine like terms: 9x + 10x = 19x -4 + 19x + -1x2 = 4 + -10x + x2 + -4 + 10x + -1x2 Reorder the terms: -4 + 19x + -1x2 = 4 + -4 + -10x + 10x + x2 + -1x2 Combine like terms: 4 + -4 = 0 -4 + 19x + -1x2 = 0 + -10x + 10x + x2 + -1x2 -4 + 19x + -1x2 = -10x + 10x + x2 + -1x2 Combine like terms: -10x + 10x = 0 -4 + 19x + -1x2 = 0 + x2 + -1x2 -4 + 19x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -4 + 19x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -19x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -19x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -19x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -19x + x2 = 0 + -4 -19x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -19x + x2 = -4 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -4 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -4 + 90.25 Combine like terms: -4 + 90.25 = 86.25 90.25 + -19x + x2 = 86.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 86.25 Calculate the square root of the right side: 9.287087811 Break this problem into two subproblems by setting (x + -9.5) equal to 9.287087811 and -9.287087811.Subproblem 1
x + -9.5 = 9.287087811 Simplifying x + -9.5 = 9.287087811 Reorder the terms: -9.5 + x = 9.287087811 Solving -9.5 + x = 9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 9.287087811 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 9.287087811 + 9.5 x = 9.287087811 + 9.5 Combine like terms: 9.287087811 + 9.5 = 18.787087811 x = 18.787087811 Simplifying x = 18.787087811Subproblem 2
x + -9.5 = -9.287087811 Simplifying x + -9.5 = -9.287087811 Reorder the terms: -9.5 + x = -9.287087811 Solving -9.5 + x = -9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -9.287087811 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -9.287087811 + 9.5 x = -9.287087811 + 9.5 Combine like terms: -9.287087811 + 9.5 = 0.212912189 x = 0.212912189 Simplifying x = 0.212912189Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.787087811, 0.212912189}
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