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Simplifying 4.905x2 + -4x + -22 = 0 Reorder the terms: -22 + -4x + 4.905x2 = 0 Solving -22 + -4x + 4.905x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -4.485219164 + -0.8154943935x + x2 = 0 Move the constant term to the right: Add '4.485219164' to each side of the equation. -4.485219164 + -0.8154943935x + 4.485219164 + x2 = 0 + 4.485219164 Reorder the terms: -4.485219164 + 4.485219164 + -0.8154943935x + x2 = 0 + 4.485219164 Combine like terms: -4.485219164 + 4.485219164 = 0.000000000 0.000000000 + -0.8154943935x + x2 = 0 + 4.485219164 -0.8154943935x + x2 = 0 + 4.485219164 Combine like terms: 0 + 4.485219164 = 4.485219164 -0.8154943935x + x2 = 4.485219164 The x term is -0.8154943935x. Take half its coefficient (-0.4077471968). Square it (0.1662577765) and add it to both sides. Add '0.1662577765' to each side of the equation. -0.8154943935x + 0.1662577765 + x2 = 4.485219164 + 0.1662577765 Reorder the terms: 0.1662577765 + -0.8154943935x + x2 = 4.485219164 + 0.1662577765 Combine like terms: 4.485219164 + 0.1662577765 = 4.6514769405 0.1662577765 + -0.8154943935x + x2 = 4.6514769405 Factor a perfect square on the left side: (x + -0.4077471968)(x + -0.4077471968) = 4.6514769405 Calculate the square root of the right side: 2.156728295 Break this problem into two subproblems by setting (x + -0.4077471968) equal to 2.156728295 and -2.156728295.Subproblem 1
x + -0.4077471968 = 2.156728295 Simplifying x + -0.4077471968 = 2.156728295 Reorder the terms: -0.4077471968 + x = 2.156728295 Solving -0.4077471968 + x = 2.156728295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4077471968' to each side of the equation. -0.4077471968 + 0.4077471968 + x = 2.156728295 + 0.4077471968 Combine like terms: -0.4077471968 + 0.4077471968 = 0.0000000000 0.0000000000 + x = 2.156728295 + 0.4077471968 x = 2.156728295 + 0.4077471968 Combine like terms: 2.156728295 + 0.4077471968 = 2.5644754918 x = 2.5644754918 Simplifying x = 2.5644754918Subproblem 2
x + -0.4077471968 = -2.156728295 Simplifying x + -0.4077471968 = -2.156728295 Reorder the terms: -0.4077471968 + x = -2.156728295 Solving -0.4077471968 + x = -2.156728295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4077471968' to each side of the equation. -0.4077471968 + 0.4077471968 + x = -2.156728295 + 0.4077471968 Combine like terms: -0.4077471968 + 0.4077471968 = 0.0000000000 0.0000000000 + x = -2.156728295 + 0.4077471968 x = -2.156728295 + 0.4077471968 Combine like terms: -2.156728295 + 0.4077471968 = -1.7489810982 x = -1.7489810982 Simplifying x = -1.7489810982Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5644754918, -1.7489810982}
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