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Simplifying -16.33333333x2 + 144.6666667x + 6 = 0 Reorder the terms: 6 + 144.6666667x + -16.33333333x2 = 0 Solving 6 + 144.6666667x + -16.33333333x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16.33333333 the coefficient of the squared term: Divide each side by '-16.33333333'. -0.3673469389 + -8.857142861x + x2 = 0 Move the constant term to the right: Add '0.3673469389' to each side of the equation. -0.3673469389 + -8.857142861x + 0.3673469389 + x2 = 0 + 0.3673469389 Reorder the terms: -0.3673469389 + 0.3673469389 + -8.857142861x + x2 = 0 + 0.3673469389 Combine like terms: -0.3673469389 + 0.3673469389 = 0.0000000000 0.0000000000 + -8.857142861x + x2 = 0 + 0.3673469389 -8.857142861x + x2 = 0 + 0.3673469389 Combine like terms: 0 + 0.3673469389 = 0.3673469389 -8.857142861x + x2 = 0.3673469389 The x term is -8.857142861x. Take half its coefficient (-4.428571431). Square it (19.61224492) and add it to both sides. Add '19.61224492' to each side of the equation. -8.857142861x + 19.61224492 + x2 = 0.3673469389 + 19.61224492 Reorder the terms: 19.61224492 + -8.857142861x + x2 = 0.3673469389 + 19.61224492 Combine like terms: 0.3673469389 + 19.61224492 = 19.9795918589 19.61224492 + -8.857142861x + x2 = 19.9795918589 Factor a perfect square on the left side: (x + -4.428571431)(x + -4.428571431) = 19.9795918589 Calculate the square root of the right side: 4.469853673 Break this problem into two subproblems by setting (x + -4.428571431) equal to 4.469853673 and -4.469853673.Subproblem 1
x + -4.428571431 = 4.469853673 Simplifying x + -4.428571431 = 4.469853673 Reorder the terms: -4.428571431 + x = 4.469853673 Solving -4.428571431 + x = 4.469853673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.428571431' to each side of the equation. -4.428571431 + 4.428571431 + x = 4.469853673 + 4.428571431 Combine like terms: -4.428571431 + 4.428571431 = 0.000000000 0.000000000 + x = 4.469853673 + 4.428571431 x = 4.469853673 + 4.428571431 Combine like terms: 4.469853673 + 4.428571431 = 8.898425104 x = 8.898425104 Simplifying x = 8.898425104Subproblem 2
x + -4.428571431 = -4.469853673 Simplifying x + -4.428571431 = -4.469853673 Reorder the terms: -4.428571431 + x = -4.469853673 Solving -4.428571431 + x = -4.469853673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.428571431' to each side of the equation. -4.428571431 + 4.428571431 + x = -4.469853673 + 4.428571431 Combine like terms: -4.428571431 + 4.428571431 = 0.000000000 0.000000000 + x = -4.469853673 + 4.428571431 x = -4.469853673 + 4.428571431 Combine like terms: -4.469853673 + 4.428571431 = -0.041282242 x = -0.041282242 Simplifying x = -0.041282242Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.898425104, -0.041282242}
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