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Simplifying 5x2 + -22x + 20 = 0 Reorder the terms: 20 + -22x + 5x2 = 0 Solving 20 + -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'. 4 + -4.4x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -4.4x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -4.4x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -4.4x + x2 = 0 + -4 -4.4x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -4.4x + x2 = -4 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 = -4 + 4.84 Reorder the terms: 4.84 + -4.4x + x2 = -4 + 4.84 Combine like terms: -4 + 4.84 = 0.84 4.84 + -4.4x + x2 = 0.84 Factor a perfect square on the left side: (x + -2.2)(x + -2.2) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (x + -2.2) equal to 0.916515139 and -0.916515139.Subproblem 1
x + -2.2 = 0.916515139 Simplifying x + -2.2 = 0.916515139 Reorder the terms: -2.2 + x = 0.916515139 Solving -2.2 + x = 0.916515139 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 = 0.916515139 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 0.916515139 + 2.2 x = 0.916515139 + 2.2 Combine like terms: 0.916515139 + 2.2 = 3.116515139 x = 3.116515139 Simplifying x = 3.116515139Subproblem 2
x + -2.2 = -0.916515139 Simplifying x + -2.2 = -0.916515139 Reorder the terms: -2.2 + x = -0.916515139 Solving -2.2 + x = -0.916515139 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 = -0.916515139 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -0.916515139 + 2.2 x = -0.916515139 + 2.2 Combine like terms: -0.916515139 + 2.2 = 1.283484861 x = 1.283484861 Simplifying x = 1.283484861Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.116515139, 1.283484861}
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