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Simplifying x2 + -22x + 1.90 = 0 Reorder the terms: 1.90 + -22x + x2 = 0 Solving 1.90 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1.90' to each side of the equation. 1.90 + -22x + -1.90 + x2 = 0 + -1.90 Reorder the terms: 1.90 + -1.90 + -22x + x2 = 0 + -1.90 Combine like terms: 1.90 + -1.90 = 0.00 0.00 + -22x + x2 = 0 + -1.90 -22x + x2 = 0 + -1.90 Combine like terms: 0 + -1.90 = -1.9 -22x + x2 = -1.9 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = -1.9 + 121 Reorder the terms: 121 + -22x + x2 = -1.9 + 121 Combine like terms: -1.9 + 121 = 119.1 121 + -22x + x2 = 119.1 Factor a perfect square on the left side: (x + -11)(x + -11) = 119.1 Calculate the square root of the right side: 10.913294645 Break this problem into two subproblems by setting (x + -11) equal to 10.913294645 and -10.913294645.Subproblem 1
x + -11 = 10.913294645 Simplifying x + -11 = 10.913294645 Reorder the terms: -11 + x = 10.913294645 Solving -11 + x = 10.913294645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 10.913294645 + 11 Combine like terms: -11 + 11 = 0 0 + x = 10.913294645 + 11 x = 10.913294645 + 11 Combine like terms: 10.913294645 + 11 = 21.913294645 x = 21.913294645 Simplifying x = 21.913294645Subproblem 2
x + -11 = -10.913294645 Simplifying x + -11 = -10.913294645 Reorder the terms: -11 + x = -10.913294645 Solving -11 + x = -10.913294645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -10.913294645 + 11 Combine like terms: -11 + 11 = 0 0 + x = -10.913294645 + 11 x = -10.913294645 + 11 Combine like terms: -10.913294645 + 11 = 0.086705355 x = 0.086705355 Simplifying x = 0.086705355Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.913294645, 0.086705355}
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