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Simplifying 17x2 + -15x + -4 = 0 Reorder the terms: -4 + -15x + 17x2 = 0 Solving -4 + -15x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.2352941176 + -0.8823529412x + x2 = 0 Move the constant term to the right: Add '0.2352941176' to each side of the equation. -0.2352941176 + -0.8823529412x + 0.2352941176 + x2 = 0 + 0.2352941176 Reorder the terms: -0.2352941176 + 0.2352941176 + -0.8823529412x + x2 = 0 + 0.2352941176 Combine like terms: -0.2352941176 + 0.2352941176 = 0.0000000000 0.0000000000 + -0.8823529412x + x2 = 0 + 0.2352941176 -0.8823529412x + x2 = 0 + 0.2352941176 Combine like terms: 0 + 0.2352941176 = 0.2352941176 -0.8823529412x + x2 = 0.2352941176 The x term is -0.8823529412x. Take half its coefficient (-0.4411764706). Square it (0.1946366782) and add it to both sides. Add '0.1946366782' to each side of the equation. -0.8823529412x + 0.1946366782 + x2 = 0.2352941176 + 0.1946366782 Reorder the terms: 0.1946366782 + -0.8823529412x + x2 = 0.2352941176 + 0.1946366782 Combine like terms: 0.2352941176 + 0.1946366782 = 0.4299307958 0.1946366782 + -0.8823529412x + x2 = 0.4299307958 Factor a perfect square on the left side: (x + -0.4411764706)(x + -0.4411764706) = 0.4299307958 Calculate the square root of the right side: 0.655691083 Break this problem into two subproblems by setting (x + -0.4411764706) equal to 0.655691083 and -0.655691083.Subproblem 1
x + -0.4411764706 = 0.655691083 Simplifying x + -0.4411764706 = 0.655691083 Reorder the terms: -0.4411764706 + x = 0.655691083 Solving -0.4411764706 + x = 0.655691083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4411764706' to each side of the equation. -0.4411764706 + 0.4411764706 + x = 0.655691083 + 0.4411764706 Combine like terms: -0.4411764706 + 0.4411764706 = 0.0000000000 0.0000000000 + x = 0.655691083 + 0.4411764706 x = 0.655691083 + 0.4411764706 Combine like terms: 0.655691083 + 0.4411764706 = 1.0968675536 x = 1.0968675536 Simplifying x = 1.0968675536Subproblem 2
x + -0.4411764706 = -0.655691083 Simplifying x + -0.4411764706 = -0.655691083 Reorder the terms: -0.4411764706 + x = -0.655691083 Solving -0.4411764706 + x = -0.655691083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4411764706' to each side of the equation. -0.4411764706 + 0.4411764706 + x = -0.655691083 + 0.4411764706 Combine like terms: -0.4411764706 + 0.4411764706 = 0.0000000000 0.0000000000 + x = -0.655691083 + 0.4411764706 x = -0.655691083 + 0.4411764706 Combine like terms: -0.655691083 + 0.4411764706 = -0.2145146124 x = -0.2145146124 Simplifying x = -0.2145146124Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0968675536, -0.2145146124}
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