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Simplifying 4x2 + -22x + 17 = 0 Reorder the terms: 17 + -22x + 4x2 = 0 Solving 17 + -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'. 4.25 + -5.5x + x2 = 0 Move the constant term to the right: Add '-4.25' to each side of the equation. 4.25 + -5.5x + -4.25 + x2 = 0 + -4.25 Reorder the terms: 4.25 + -4.25 + -5.5x + x2 = 0 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + -5.5x + x2 = 0 + -4.25 -5.5x + x2 = 0 + -4.25 Combine like terms: 0 + -4.25 = -4.25 -5.5x + x2 = -4.25 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 = -4.25 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -4.25 + 7.5625 Combine like terms: -4.25 + 7.5625 = 3.3125 7.5625 + -5.5x + x2 = 3.3125 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 3.3125 Calculate the square root of the right side: 1.820027472 Break this problem into two subproblems by setting (x + -2.75) equal to 1.820027472 and -1.820027472.Subproblem 1
x + -2.75 = 1.820027472 Simplifying x + -2.75 = 1.820027472 Reorder the terms: -2.75 + x = 1.820027472 Solving -2.75 + x = 1.820027472 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 = 1.820027472 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 1.820027472 + 2.75 x = 1.820027472 + 2.75 Combine like terms: 1.820027472 + 2.75 = 4.570027472 x = 4.570027472 Simplifying x = 4.570027472Subproblem 2
x + -2.75 = -1.820027472 Simplifying x + -2.75 = -1.820027472 Reorder the terms: -2.75 + x = -1.820027472 Solving -2.75 + x = -1.820027472 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 = -1.820027472 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -1.820027472 + 2.75 x = -1.820027472 + 2.75 Combine like terms: -1.820027472 + 2.75 = 0.929972528 x = 0.929972528 Simplifying x = 0.929972528Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.570027472, 0.929972528}
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