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Simplifying 41x(x) + -164x + -12x + 48 = 4x(x) + 3x(x) + -64x + -48 Multiply x * x 41x2 + -164x + -12x + 48 = 4x(x) + 3x(x) + -64x + -48 Reorder the terms: 48 + -164x + -12x + 41x2 = 4x(x) + 3x(x) + -64x + -48 Combine like terms: -164x + -12x = -176x 48 + -176x + 41x2 = 4x(x) + 3x(x) + -64x + -48 Multiply x * x 48 + -176x + 41x2 = 4x2 + 3x(x) + -64x + -48 Multiply x * x 48 + -176x + 41x2 = 4x2 + 3x2 + -64x + -48 Reorder the terms: 48 + -176x + 41x2 = -48 + -64x + 4x2 + 3x2 Combine like terms: 4x2 + 3x2 = 7x2 48 + -176x + 41x2 = -48 + -64x + 7x2 Solving 48 + -176x + 41x2 = -48 + -64x + 7x2 Solving for variable 'x'. Reorder the terms: 48 + 48 + -176x + 64x + 41x2 + -7x2 = -48 + -64x + 7x2 + 48 + 64x + -7x2 Combine like terms: 48 + 48 = 96 96 + -176x + 64x + 41x2 + -7x2 = -48 + -64x + 7x2 + 48 + 64x + -7x2 Combine like terms: -176x + 64x = -112x 96 + -112x + 41x2 + -7x2 = -48 + -64x + 7x2 + 48 + 64x + -7x2 Combine like terms: 41x2 + -7x2 = 34x2 96 + -112x + 34x2 = -48 + -64x + 7x2 + 48 + 64x + -7x2 Reorder the terms: 96 + -112x + 34x2 = -48 + 48 + -64x + 64x + 7x2 + -7x2 Combine like terms: -48 + 48 = 0 96 + -112x + 34x2 = 0 + -64x + 64x + 7x2 + -7x2 96 + -112x + 34x2 = -64x + 64x + 7x2 + -7x2 Combine like terms: -64x + 64x = 0 96 + -112x + 34x2 = 0 + 7x2 + -7x2 96 + -112x + 34x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 96 + -112x + 34x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(48 + -56x + 17x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(48 + -56x + 17x2)' equal to zero and attempt to solve: Simplifying 48 + -56x + 17x2 = 0 Solving 48 + -56x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 2.823529412 + -3.294117647x + x2 = 0 Move the constant term to the right: Add '-2.823529412' to each side of the equation. 2.823529412 + -3.294117647x + -2.823529412 + x2 = 0 + -2.823529412 Reorder the terms: 2.823529412 + -2.823529412 + -3.294117647x + x2 = 0 + -2.823529412 Combine like terms: 2.823529412 + -2.823529412 = 0.000000000 0.000000000 + -3.294117647x + x2 = 0 + -2.823529412 -3.294117647x + x2 = 0 + -2.823529412 Combine like terms: 0 + -2.823529412 = -2.823529412 -3.294117647x + x2 = -2.823529412 The x term is -3.294117647x. Take half its coefficient (-1.647058824). Square it (2.712802770) and add it to both sides. Add '2.712802770' to each side of the equation. -3.294117647x + 2.712802770 + x2 = -2.823529412 + 2.712802770 Reorder the terms: 2.712802770 + -3.294117647x + x2 = -2.823529412 + 2.712802770 Combine like terms: -2.823529412 + 2.712802770 = -0.110726642 2.712802770 + -3.294117647x + x2 = -0.110726642 Factor a perfect square on the left side: (x + -1.647058824)(x + -1.647058824) = -0.110726642 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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