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Simplifying -2 = -17x2 + 19x Reorder the terms: -2 = 19x + -17x2 Solving -2 = 19x + -17x2 Solving for variable 'x'. Reorder the terms: -2 + -19x + 17x2 = 19x + -19x + -17x2 + 17x2 Combine like terms: 19x + -19x = 0 -2 + -19x + 17x2 = 0 + -17x2 + 17x2 -2 + -19x + 17x2 = -17x2 + 17x2 Combine like terms: -17x2 + 17x2 = 0 -2 + -19x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.1176470588 + -1.117647059x + x2 = 0 Move the constant term to the right: Add '0.1176470588' to each side of the equation. -0.1176470588 + -1.117647059x + 0.1176470588 + x2 = 0 + 0.1176470588 Reorder the terms: -0.1176470588 + 0.1176470588 + -1.117647059x + x2 = 0 + 0.1176470588 Combine like terms: -0.1176470588 + 0.1176470588 = 0.0000000000 0.0000000000 + -1.117647059x + x2 = 0 + 0.1176470588 -1.117647059x + x2 = 0 + 0.1176470588 Combine like terms: 0 + 0.1176470588 = 0.1176470588 -1.117647059x + x2 = 0.1176470588 The x term is -1.117647059x. Take half its coefficient (-0.5588235295). Square it (0.3122837371) and add it to both sides. Add '0.3122837371' to each side of the equation. -1.117647059x + 0.3122837371 + x2 = 0.1176470588 + 0.3122837371 Reorder the terms: 0.3122837371 + -1.117647059x + x2 = 0.1176470588 + 0.3122837371 Combine like terms: 0.1176470588 + 0.3122837371 = 0.4299307959 0.3122837371 + -1.117647059x + x2 = 0.4299307959 Factor a perfect square on the left side: (x + -0.5588235295)(x + -0.5588235295) = 0.4299307959 Calculate the square root of the right side: 0.655691083 Break this problem into two subproblems by setting (x + -0.5588235295) equal to 0.655691083 and -0.655691083.Subproblem 1
x + -0.5588235295 = 0.655691083 Simplifying x + -0.5588235295 = 0.655691083 Reorder the terms: -0.5588235295 + x = 0.655691083 Solving -0.5588235295 + x = 0.655691083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5588235295' to each side of the equation. -0.5588235295 + 0.5588235295 + x = 0.655691083 + 0.5588235295 Combine like terms: -0.5588235295 + 0.5588235295 = 0.0000000000 0.0000000000 + x = 0.655691083 + 0.5588235295 x = 0.655691083 + 0.5588235295 Combine like terms: 0.655691083 + 0.5588235295 = 1.2145146125 x = 1.2145146125 Simplifying x = 1.2145146125Subproblem 2
x + -0.5588235295 = -0.655691083 Simplifying x + -0.5588235295 = -0.655691083 Reorder the terms: -0.5588235295 + x = -0.655691083 Solving -0.5588235295 + x = -0.655691083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5588235295' to each side of the equation. -0.5588235295 + 0.5588235295 + x = -0.655691083 + 0.5588235295 Combine like terms: -0.5588235295 + 0.5588235295 = 0.0000000000 0.0000000000 + x = -0.655691083 + 0.5588235295 x = -0.655691083 + 0.5588235295 Combine like terms: -0.655691083 + 0.5588235295 = -0.0968675535 x = -0.0968675535 Simplifying x = -0.0968675535Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2145146125, -0.0968675535}
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