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Simplifying 17x2 + -61x + 48 = 0 Reorder the terms: 48 + -61x + 17x2 = 0 Solving 48 + -61x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 2.823529412 + -3.588235294x + x2 = 0 Move the constant term to the right: Add '-2.823529412' to each side of the equation. 2.823529412 + -3.588235294x + -2.823529412 + x2 = 0 + -2.823529412 Reorder the terms: 2.823529412 + -2.823529412 + -3.588235294x + x2 = 0 + -2.823529412 Combine like terms: 2.823529412 + -2.823529412 = 0.000000000 0.000000000 + -3.588235294x + x2 = 0 + -2.823529412 -3.588235294x + x2 = 0 + -2.823529412 Combine like terms: 0 + -2.823529412 = -2.823529412 -3.588235294x + x2 = -2.823529412 The x term is -3.588235294x. Take half its coefficient (-1.794117647). Square it (3.218858131) and add it to both sides. Add '3.218858131' to each side of the equation. -3.588235294x + 3.218858131 + x2 = -2.823529412 + 3.218858131 Reorder the terms: 3.218858131 + -3.588235294x + x2 = -2.823529412 + 3.218858131 Combine like terms: -2.823529412 + 3.218858131 = 0.395328719 3.218858131 + -3.588235294x + x2 = 0.395328719 Factor a perfect square on the left side: (x + -1.794117647)(x + -1.794117647) = 0.395328719 Calculate the square root of the right side: 0.628751715 Break this problem into two subproblems by setting (x + -1.794117647) equal to 0.628751715 and -0.628751715.Subproblem 1
x + -1.794117647 = 0.628751715 Simplifying x + -1.794117647 = 0.628751715 Reorder the terms: -1.794117647 + x = 0.628751715 Solving -1.794117647 + x = 0.628751715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.794117647' to each side of the equation. -1.794117647 + 1.794117647 + x = 0.628751715 + 1.794117647 Combine like terms: -1.794117647 + 1.794117647 = 0.000000000 0.000000000 + x = 0.628751715 + 1.794117647 x = 0.628751715 + 1.794117647 Combine like terms: 0.628751715 + 1.794117647 = 2.422869362 x = 2.422869362 Simplifying x = 2.422869362Subproblem 2
x + -1.794117647 = -0.628751715 Simplifying x + -1.794117647 = -0.628751715 Reorder the terms: -1.794117647 + x = -0.628751715 Solving -1.794117647 + x = -0.628751715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.794117647' to each side of the equation. -1.794117647 + 1.794117647 + x = -0.628751715 + 1.794117647 Combine like terms: -1.794117647 + 1.794117647 = 0.000000000 0.000000000 + x = -0.628751715 + 1.794117647 x = -0.628751715 + 1.794117647 Combine like terms: -0.628751715 + 1.794117647 = 1.165365932 x = 1.165365932 Simplifying x = 1.165365932Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.422869362, 1.165365932}
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