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Simplifying 0 = 4.3x2 + -2.2x + -2.6 Reorder the terms: 0 = -2.6 + -2.2x + 4.3x2 Solving 0 = -2.6 + -2.2x + 4.3x2 Solving for variable 'x'. Combine like terms: 0 + 2.6 = 2.6 2.6 + 2.2x + -4.3x2 = -2.6 + -2.2x + 4.3x2 + 2.6 + 2.2x + -4.3x2 Reorder the terms: 2.6 + 2.2x + -4.3x2 = -2.6 + 2.6 + -2.2x + 2.2x + 4.3x2 + -4.3x2 Combine like terms: -2.6 + 2.6 = 0.0 2.6 + 2.2x + -4.3x2 = 0.0 + -2.2x + 2.2x + 4.3x2 + -4.3x2 2.6 + 2.2x + -4.3x2 = -2.2x + 2.2x + 4.3x2 + -4.3x2 Combine like terms: -2.2x + 2.2x = 0.0 2.6 + 2.2x + -4.3x2 = 0.0 + 4.3x2 + -4.3x2 2.6 + 2.2x + -4.3x2 = 4.3x2 + -4.3x2 Combine like terms: 4.3x2 + -4.3x2 = 0.0 2.6 + 2.2x + -4.3x2 = 0.0 Begin completing the square. Divide all terms by -4.3 the coefficient of the squared term: Divide each side by '-4.3'. -0.6046511628 + -0.511627907x + x2 = 0 Move the constant term to the right: Add '0.6046511628' to each side of the equation. -0.6046511628 + -0.511627907x + 0.6046511628 + x2 = 0 + 0.6046511628 Reorder the terms: -0.6046511628 + 0.6046511628 + -0.511627907x + x2 = 0 + 0.6046511628 Combine like terms: -0.6046511628 + 0.6046511628 = 0.0000000000 0.0000000000 + -0.511627907x + x2 = 0 + 0.6046511628 -0.511627907x + x2 = 0 + 0.6046511628 Combine like terms: 0 + 0.6046511628 = 0.6046511628 -0.511627907x + x2 = 0.6046511628 The x term is -0.511627907x. Take half its coefficient (-0.2558139535). Square it (0.06544077881) and add it to both sides. Add '0.06544077881' to each side of the equation. -0.511627907x + 0.06544077881 + x2 = 0.6046511628 + 0.06544077881 Reorder the terms: 0.06544077881 + -0.511627907x + x2 = 0.6046511628 + 0.06544077881 Combine like terms: 0.6046511628 + 0.06544077881 = 0.67009194161 0.06544077881 + -0.511627907x + x2 = 0.67009194161 Factor a perfect square on the left side: (x + -0.2558139535)(x + -0.2558139535) = 0.67009194161 Calculate the square root of the right side: 0.818591438 Break this problem into two subproblems by setting (x + -0.2558139535) equal to 0.818591438 and -0.818591438.Subproblem 1
x + -0.2558139535 = 0.818591438 Simplifying x + -0.2558139535 = 0.818591438 Reorder the terms: -0.2558139535 + x = 0.818591438 Solving -0.2558139535 + x = 0.818591438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2558139535' to each side of the equation. -0.2558139535 + 0.2558139535 + x = 0.818591438 + 0.2558139535 Combine like terms: -0.2558139535 + 0.2558139535 = 0.0000000000 0.0000000000 + x = 0.818591438 + 0.2558139535 x = 0.818591438 + 0.2558139535 Combine like terms: 0.818591438 + 0.2558139535 = 1.0744053915 x = 1.0744053915 Simplifying x = 1.0744053915Subproblem 2
x + -0.2558139535 = -0.818591438 Simplifying x + -0.2558139535 = -0.818591438 Reorder the terms: -0.2558139535 + x = -0.818591438 Solving -0.2558139535 + x = -0.818591438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2558139535' to each side of the equation. -0.2558139535 + 0.2558139535 + x = -0.818591438 + 0.2558139535 Combine like terms: -0.2558139535 + 0.2558139535 = 0.0000000000 0.0000000000 + x = -0.818591438 + 0.2558139535 x = -0.818591438 + 0.2558139535 Combine like terms: -0.818591438 + 0.2558139535 = -0.5627774845 x = -0.5627774845 Simplifying x = -0.5627774845Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0744053915, -0.5627774845}
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