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Simplifying 5x2 + -22x + 6 = 0 Reorder the terms: 6 + -22x + 5x2 = 0 Solving 6 + -22x + 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'. 1.2 + -4.4x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -4.4x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -4.4x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -4.4x + x2 = 0 + -1.2 -4.4x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -4.4x + x2 = -1.2 The x term is -4.4x. Take half its coefficient (-2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. -4.4x + 4.84 + x2 = -1.2 + 4.84 Reorder the terms: 4.84 + -4.4x + x2 = -1.2 + 4.84 Combine like terms: -1.2 + 4.84 = 3.64 4.84 + -4.4x + x2 = 3.64 Factor a perfect square on the left side: (x + -2.2)(x + -2.2) = 3.64 Calculate the square root of the right side: 1.907878403 Break this problem into two subproblems by setting (x + -2.2) equal to 1.907878403 and -1.907878403.Subproblem 1
x + -2.2 = 1.907878403 Simplifying x + -2.2 = 1.907878403 Reorder the terms: -2.2 + x = 1.907878403 Solving -2.2 + x = 1.907878403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = 1.907878403 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 1.907878403 + 2.2 x = 1.907878403 + 2.2 Combine like terms: 1.907878403 + 2.2 = 4.107878403 x = 4.107878403 Simplifying x = 4.107878403Subproblem 2
x + -2.2 = -1.907878403 Simplifying x + -2.2 = -1.907878403 Reorder the terms: -2.2 + x = -1.907878403 Solving -2.2 + x = -1.907878403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = -1.907878403 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -1.907878403 + 2.2 x = -1.907878403 + 2.2 Combine like terms: -1.907878403 + 2.2 = 0.292121597 x = 0.292121597 Simplifying x = 0.292121597Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.107878403, 0.292121597}
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