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Simplifying 0 = 0.56x2 + -5x + 7.56 Reorder the terms: 0 = 7.56 + -5x + 0.56x2 Solving 0 = 7.56 + -5x + 0.56x2 Solving for variable 'x'. Combine like terms: 0 + -7.56 = -7.56 -7.56 + 5x + -0.56x2 = 7.56 + -5x + 0.56x2 + -7.56 + 5x + -0.56x2 Reorder the terms: -7.56 + 5x + -0.56x2 = 7.56 + -7.56 + -5x + 5x + 0.56x2 + -0.56x2 Combine like terms: 7.56 + -7.56 = 0.00 -7.56 + 5x + -0.56x2 = 0.00 + -5x + 5x + 0.56x2 + -0.56x2 -7.56 + 5x + -0.56x2 = -5x + 5x + 0.56x2 + -0.56x2 Combine like terms: -5x + 5x = 0 -7.56 + 5x + -0.56x2 = 0 + 0.56x2 + -0.56x2 -7.56 + 5x + -0.56x2 = 0.56x2 + -0.56x2 Combine like terms: 0.56x2 + -0.56x2 = 0.00 -7.56 + 5x + -0.56x2 = 0.00 Begin completing the square. Divide all terms by -0.56 the coefficient of the squared term: Divide each side by '-0.56'. 13.5 + -8.928571429x + x2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + -8.928571429x + -13.5 + x2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + -8.928571429x + x2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + -8.928571429x + x2 = 0 + -13.5 -8.928571429x + x2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 -8.928571429x + x2 = -13.5 The x term is -8.928571429x. Take half its coefficient (-4.464285715). Square it (19.92984695) and add it to both sides. Add '19.92984695' to each side of the equation. -8.928571429x + 19.92984695 + x2 = -13.5 + 19.92984695 Reorder the terms: 19.92984695 + -8.928571429x + x2 = -13.5 + 19.92984695 Combine like terms: -13.5 + 19.92984695 = 6.42984695 19.92984695 + -8.928571429x + x2 = 6.42984695 Factor a perfect square on the left side: (x + -4.464285715)(x + -4.464285715) = 6.42984695 Calculate the square root of the right side: 2.535714288 Break this problem into two subproblems by setting (x + -4.464285715) equal to 2.535714288 and -2.535714288.Subproblem 1
x + -4.464285715 = 2.535714288 Simplifying x + -4.464285715 = 2.535714288 Reorder the terms: -4.464285715 + x = 2.535714288 Solving -4.464285715 + x = 2.535714288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.464285715' to each side of the equation. -4.464285715 + 4.464285715 + x = 2.535714288 + 4.464285715 Combine like terms: -4.464285715 + 4.464285715 = 0.000000000 0.000000000 + x = 2.535714288 + 4.464285715 x = 2.535714288 + 4.464285715 Combine like terms: 2.535714288 + 4.464285715 = 7.000000003 x = 7.000000003 Simplifying x = 7.000000003Subproblem 2
x + -4.464285715 = -2.535714288 Simplifying x + -4.464285715 = -2.535714288 Reorder the terms: -4.464285715 + x = -2.535714288 Solving -4.464285715 + x = -2.535714288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.464285715' to each side of the equation. -4.464285715 + 4.464285715 + x = -2.535714288 + 4.464285715 Combine like terms: -4.464285715 + 4.464285715 = 0.000000000 0.000000000 + x = -2.535714288 + 4.464285715 x = -2.535714288 + 4.464285715 Combine like terms: -2.535714288 + 4.464285715 = 1.928571427 x = 1.928571427 Simplifying x = 1.928571427Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.000000003, 1.928571427}
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