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Simplifying 0 = 17x2 + -33 + 9x Reorder the terms: 0 = -33 + 9x + 17x2 Solving 0 = -33 + 9x + 17x2 Solving for variable 'x'. Combine like terms: 0 + 33 = 33 33 + -9x + -17x2 = -33 + 9x + 17x2 + 33 + -9x + -17x2 Reorder the terms: 33 + -9x + -17x2 = -33 + 33 + 9x + -9x + 17x2 + -17x2 Combine like terms: -33 + 33 = 0 33 + -9x + -17x2 = 0 + 9x + -9x + 17x2 + -17x2 33 + -9x + -17x2 = 9x + -9x + 17x2 + -17x2 Combine like terms: 9x + -9x = 0 33 + -9x + -17x2 = 0 + 17x2 + -17x2 33 + -9x + -17x2 = 17x2 + -17x2 Combine like terms: 17x2 + -17x2 = 0 33 + -9x + -17x2 = 0 Begin completing the square. Divide all terms by -17 the coefficient of the squared term: Divide each side by '-17'. -1.941176471 + 0.5294117647x + x2 = 0 Move the constant term to the right: Add '1.941176471' to each side of the equation. -1.941176471 + 0.5294117647x + 1.941176471 + x2 = 0 + 1.941176471 Reorder the terms: -1.941176471 + 1.941176471 + 0.5294117647x + x2 = 0 + 1.941176471 Combine like terms: -1.941176471 + 1.941176471 = 0.000000000 0.000000000 + 0.5294117647x + x2 = 0 + 1.941176471 0.5294117647x + x2 = 0 + 1.941176471 Combine like terms: 0 + 1.941176471 = 1.941176471 0.5294117647x + x2 = 1.941176471 The x term is 0.5294117647x. Take half its coefficient (0.2647058824). Square it (0.07006920418) and add it to both sides. Add '0.07006920418' to each side of the equation. 0.5294117647x + 0.07006920418 + x2 = 1.941176471 + 0.07006920418 Reorder the terms: 0.07006920418 + 0.5294117647x + x2 = 1.941176471 + 0.07006920418 Combine like terms: 1.941176471 + 0.07006920418 = 2.01124567518 0.07006920418 + 0.5294117647x + x2 = 2.01124567518 Factor a perfect square on the left side: (x + 0.2647058824)(x + 0.2647058824) = 2.01124567518 Calculate the square root of the right side: 1.418183936 Break this problem into two subproblems by setting (x + 0.2647058824) equal to 1.418183936 and -1.418183936.Subproblem 1
x + 0.2647058824 = 1.418183936 Simplifying x + 0.2647058824 = 1.418183936 Reorder the terms: 0.2647058824 + x = 1.418183936 Solving 0.2647058824 + x = 1.418183936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2647058824' to each side of the equation. 0.2647058824 + -0.2647058824 + x = 1.418183936 + -0.2647058824 Combine like terms: 0.2647058824 + -0.2647058824 = 0.0000000000 0.0000000000 + x = 1.418183936 + -0.2647058824 x = 1.418183936 + -0.2647058824 Combine like terms: 1.418183936 + -0.2647058824 = 1.1534780536 x = 1.1534780536 Simplifying x = 1.1534780536Subproblem 2
x + 0.2647058824 = -1.418183936 Simplifying x + 0.2647058824 = -1.418183936 Reorder the terms: 0.2647058824 + x = -1.418183936 Solving 0.2647058824 + x = -1.418183936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2647058824' to each side of the equation. 0.2647058824 + -0.2647058824 + x = -1.418183936 + -0.2647058824 Combine like terms: 0.2647058824 + -0.2647058824 = 0.0000000000 0.0000000000 + x = -1.418183936 + -0.2647058824 x = -1.418183936 + -0.2647058824 Combine like terms: -1.418183936 + -0.2647058824 = -1.6828898184 x = -1.6828898184 Simplifying x = -1.6828898184Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1534780536, -1.6828898184}
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