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Simplifying 4x2 + -22x + 7 = 0 Reorder the terms: 7 + -22x + 4x2 = 0 Solving 7 + -22x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + -5.5x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -5.5x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -5.5x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -5.5x + x2 = 0 + -1.75 -5.5x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -5.5x + x2 = -1.75 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -1.75 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -1.75 + 7.5625 Combine like terms: -1.75 + 7.5625 = 5.8125 7.5625 + -5.5x + x2 = 5.8125 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 5.8125 Calculate the square root of the right side: 2.41091269 Break this problem into two subproblems by setting (x + -2.75) equal to 2.41091269 and -2.41091269.Subproblem 1
x + -2.75 = 2.41091269 Simplifying x + -2.75 = 2.41091269 Reorder the terms: -2.75 + x = 2.41091269 Solving -2.75 + x = 2.41091269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 2.41091269 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 2.41091269 + 2.75 x = 2.41091269 + 2.75 Combine like terms: 2.41091269 + 2.75 = 5.16091269 x = 5.16091269 Simplifying x = 5.16091269Subproblem 2
x + -2.75 = -2.41091269 Simplifying x + -2.75 = -2.41091269 Reorder the terms: -2.75 + x = -2.41091269 Solving -2.75 + x = -2.41091269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -2.41091269 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -2.41091269 + 2.75 x = -2.41091269 + 2.75 Combine like terms: -2.41091269 + 2.75 = 0.33908731 x = 0.33908731 Simplifying x = 0.33908731Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.16091269, 0.33908731}
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