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Simplifying 17x2 = 48x + -14 Reorder the terms: 17x2 = -14 + 48x Solving 17x2 = -14 + 48x Solving for variable 'x'. Reorder the terms: 14 + -48x + 17x2 = -14 + 48x + 14 + -48x Reorder the terms: 14 + -48x + 17x2 = -14 + 14 + 48x + -48x Combine like terms: -14 + 14 = 0 14 + -48x + 17x2 = 0 + 48x + -48x 14 + -48x + 17x2 = 48x + -48x Combine like terms: 48x + -48x = 0 14 + -48x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 0.8235294118 + -2.823529412x + x2 = 0 Move the constant term to the right: Add '-0.8235294118' to each side of the equation. 0.8235294118 + -2.823529412x + -0.8235294118 + x2 = 0 + -0.8235294118 Reorder the terms: 0.8235294118 + -0.8235294118 + -2.823529412x + x2 = 0 + -0.8235294118 Combine like terms: 0.8235294118 + -0.8235294118 = 0.0000000000 0.0000000000 + -2.823529412x + x2 = 0 + -0.8235294118 -2.823529412x + x2 = 0 + -0.8235294118 Combine like terms: 0 + -0.8235294118 = -0.8235294118 -2.823529412x + x2 = -0.8235294118 The x term is -2.823529412x. Take half its coefficient (-1.411764706). Square it (1.993079585) and add it to both sides. Add '1.993079585' to each side of the equation. -2.823529412x + 1.993079585 + x2 = -0.8235294118 + 1.993079585 Reorder the terms: 1.993079585 + -2.823529412x + x2 = -0.8235294118 + 1.993079585 Combine like terms: -0.8235294118 + 1.993079585 = 1.1695501732 1.993079585 + -2.823529412x + x2 = 1.1695501732 Factor a perfect square on the left side: (x + -1.411764706)(x + -1.411764706) = 1.1695501732 Calculate the square root of the right side: 1.08145743 Break this problem into two subproblems by setting (x + -1.411764706) equal to 1.08145743 and -1.08145743.Subproblem 1
x + -1.411764706 = 1.08145743 Simplifying x + -1.411764706 = 1.08145743 Reorder the terms: -1.411764706 + x = 1.08145743 Solving -1.411764706 + x = 1.08145743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.411764706' to each side of the equation. -1.411764706 + 1.411764706 + x = 1.08145743 + 1.411764706 Combine like terms: -1.411764706 + 1.411764706 = 0.000000000 0.000000000 + x = 1.08145743 + 1.411764706 x = 1.08145743 + 1.411764706 Combine like terms: 1.08145743 + 1.411764706 = 2.493222136 x = 2.493222136 Simplifying x = 2.493222136Subproblem 2
x + -1.411764706 = -1.08145743 Simplifying x + -1.411764706 = -1.08145743 Reorder the terms: -1.411764706 + x = -1.08145743 Solving -1.411764706 + x = -1.08145743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.411764706' to each side of the equation. -1.411764706 + 1.411764706 + x = -1.08145743 + 1.411764706 Combine like terms: -1.411764706 + 1.411764706 = 0.000000000 0.000000000 + x = -1.08145743 + 1.411764706 x = -1.08145743 + 1.411764706 Combine like terms: -1.08145743 + 1.411764706 = 0.330307276 x = 0.330307276 Simplifying x = 0.330307276Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.493222136, 0.330307276}
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