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Simplifying 17x2 + 130x + 2 = 0 Reorder the terms: 2 + 130x + 17x2 = 0 Solving 2 + 130x + 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'. 0.1176470588 + 7.647058824x + x2 = 0 Move the constant term to the right: Add '-0.1176470588' to each side of the equation. 0.1176470588 + 7.647058824x + -0.1176470588 + x2 = 0 + -0.1176470588 Reorder the terms: 0.1176470588 + -0.1176470588 + 7.647058824x + x2 = 0 + -0.1176470588 Combine like terms: 0.1176470588 + -0.1176470588 = 0.0000000000 0.0000000000 + 7.647058824x + x2 = 0 + -0.1176470588 7.647058824x + x2 = 0 + -0.1176470588 Combine like terms: 0 + -0.1176470588 = -0.1176470588 7.647058824x + x2 = -0.1176470588 The x term is 7.647058824x. Take half its coefficient (3.823529412). Square it (14.61937716) and add it to both sides. Add '14.61937716' to each side of the equation. 7.647058824x + 14.61937716 + x2 = -0.1176470588 + 14.61937716 Reorder the terms: 14.61937716 + 7.647058824x + x2 = -0.1176470588 + 14.61937716 Combine like terms: -0.1176470588 + 14.61937716 = 14.5017301012 14.61937716 + 7.647058824x + x2 = 14.5017301012 Factor a perfect square on the left side: (x + 3.823529412)(x + 3.823529412) = 14.5017301012 Calculate the square root of the right side: 3.80811372 Break this problem into two subproblems by setting (x + 3.823529412) equal to 3.80811372 and -3.80811372.Subproblem 1
x + 3.823529412 = 3.80811372 Simplifying x + 3.823529412 = 3.80811372 Reorder the terms: 3.823529412 + x = 3.80811372 Solving 3.823529412 + x = 3.80811372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.823529412' to each side of the equation. 3.823529412 + -3.823529412 + x = 3.80811372 + -3.823529412 Combine like terms: 3.823529412 + -3.823529412 = 0.000000000 0.000000000 + x = 3.80811372 + -3.823529412 x = 3.80811372 + -3.823529412 Combine like terms: 3.80811372 + -3.823529412 = -0.015415692 x = -0.015415692 Simplifying x = -0.015415692Subproblem 2
x + 3.823529412 = -3.80811372 Simplifying x + 3.823529412 = -3.80811372 Reorder the terms: 3.823529412 + x = -3.80811372 Solving 3.823529412 + x = -3.80811372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.823529412' to each side of the equation. 3.823529412 + -3.823529412 + x = -3.80811372 + -3.823529412 Combine like terms: 3.823529412 + -3.823529412 = 0.000000000 0.000000000 + x = -3.80811372 + -3.823529412 x = -3.80811372 + -3.823529412 Combine like terms: -3.80811372 + -3.823529412 = -7.631643132 x = -7.631643132 Simplifying x = -7.631643132Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.015415692, -7.631643132}
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