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Simplifying 5x2 + -23x + 22 = 0 Reorder the terms: 22 + -23x + 5x2 = 0 Solving 22 + -23x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4.4 + -4.6x + x2 = 0 Move the constant term to the right: Add '-4.4' to each side of the equation. 4.4 + -4.6x + -4.4 + x2 = 0 + -4.4 Reorder the terms: 4.4 + -4.4 + -4.6x + x2 = 0 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + -4.6x + x2 = 0 + -4.4 -4.6x + x2 = 0 + -4.4 Combine like terms: 0 + -4.4 = -4.4 -4.6x + x2 = -4.4 The x term is -4.6x. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6x + 5.29 + x2 = -4.4 + 5.29 Reorder the terms: 5.29 + -4.6x + x2 = -4.4 + 5.29 Combine like terms: -4.4 + 5.29 = 0.89 5.29 + -4.6x + x2 = 0.89 Factor a perfect square on the left side: (x + -2.3)(x + -2.3) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (x + -2.3) equal to 0.943398113 and -0.943398113.Subproblem 1
x + -2.3 = 0.943398113 Simplifying x + -2.3 = 0.943398113 Reorder the terms: -2.3 + x = 0.943398113 Solving -2.3 + x = 0.943398113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = 0.943398113 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = 0.943398113 + 2.3 x = 0.943398113 + 2.3 Combine like terms: 0.943398113 + 2.3 = 3.243398113 x = 3.243398113 Simplifying x = 3.243398113Subproblem 2
x + -2.3 = -0.943398113 Simplifying x + -2.3 = -0.943398113 Reorder the terms: -2.3 + x = -0.943398113 Solving -2.3 + x = -0.943398113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = -0.943398113 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = -0.943398113 + 2.3 x = -0.943398113 + 2.3 Combine like terms: -0.943398113 + 2.3 = 1.356601887 x = 1.356601887 Simplifying x = 1.356601887Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.243398113, 1.356601887}
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