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Simplifying -22.872x2 + 2x + 1 = 0 Reorder the terms: 1 + 2x + -22.872x2 = 0 Solving 1 + 2x + -22.872x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -22.872 the coefficient of the squared term: Divide each side by '-22.872'. -0.04372158097 + -0.08744316194x + x2 = 0 Move the constant term to the right: Add '0.04372158097' to each side of the equation. -0.04372158097 + -0.08744316194x + 0.04372158097 + x2 = 0 + 0.04372158097 Reorder the terms: -0.04372158097 + 0.04372158097 + -0.08744316194x + x2 = 0 + 0.04372158097 Combine like terms: -0.04372158097 + 0.04372158097 = 0.00000000000 0.00000000000 + -0.08744316194x + x2 = 0 + 0.04372158097 -0.08744316194x + x2 = 0 + 0.04372158097 Combine like terms: 0 + 0.04372158097 = 0.04372158097 -0.08744316194x + x2 = 0.04372158097 The x term is -0.08744316194x. Take half its coefficient (-0.04372158097). Square it (0.001911576643) and add it to both sides. Add '0.001911576643' to each side of the equation. -0.08744316194x + 0.001911576643 + x2 = 0.04372158097 + 0.001911576643 Reorder the terms: 0.001911576643 + -0.08744316194x + x2 = 0.04372158097 + 0.001911576643 Combine like terms: 0.04372158097 + 0.001911576643 = 0.045633157613 0.001911576643 + -0.08744316194x + x2 = 0.045633157613 Factor a perfect square on the left side: (x + -0.04372158097)(x + -0.04372158097) = 0.045633157613 Calculate the square root of the right side: 0.213619188 Break this problem into two subproblems by setting (x + -0.04372158097) equal to 0.213619188 and -0.213619188.Subproblem 1
x + -0.04372158097 = 0.213619188 Simplifying x + -0.04372158097 = 0.213619188 Reorder the terms: -0.04372158097 + x = 0.213619188 Solving -0.04372158097 + x = 0.213619188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04372158097' to each side of the equation. -0.04372158097 + 0.04372158097 + x = 0.213619188 + 0.04372158097 Combine like terms: -0.04372158097 + 0.04372158097 = 0.00000000000 0.00000000000 + x = 0.213619188 + 0.04372158097 x = 0.213619188 + 0.04372158097 Combine like terms: 0.213619188 + 0.04372158097 = 0.25734076897 x = 0.25734076897 Simplifying x = 0.25734076897Subproblem 2
x + -0.04372158097 = -0.213619188 Simplifying x + -0.04372158097 = -0.213619188 Reorder the terms: -0.04372158097 + x = -0.213619188 Solving -0.04372158097 + x = -0.213619188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04372158097' to each side of the equation. -0.04372158097 + 0.04372158097 + x = -0.213619188 + 0.04372158097 Combine like terms: -0.04372158097 + 0.04372158097 = 0.00000000000 0.00000000000 + x = -0.213619188 + 0.04372158097 x = -0.213619188 + 0.04372158097 Combine like terms: -0.213619188 + 0.04372158097 = -0.16989760703 x = -0.16989760703 Simplifying x = -0.16989760703Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.25734076897, -0.16989760703}
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