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Simplifying 0.006x2 + -4x + 65 = 0 Reorder the terms: 65 + -4x + 0.006x2 = 0 Solving 65 + -4x + 0.006x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.006 the coefficient of the squared term: Divide each side by '0.006'. 10833.33333 + -666.6666667x + x2 = 0 Move the constant term to the right: Add '-10833.33333' to each side of the equation. 10833.33333 + -666.6666667x + -10833.33333 + x2 = 0 + -10833.33333 Reorder the terms: 10833.33333 + -10833.33333 + -666.6666667x + x2 = 0 + -10833.33333 Combine like terms: 10833.33333 + -10833.33333 = 0.00000 0.00000 + -666.6666667x + x2 = 0 + -10833.33333 -666.6666667x + x2 = 0 + -10833.33333 Combine like terms: 0 + -10833.33333 = -10833.33333 -666.6666667x + x2 = -10833.33333 The x term is -666.6666667x. Take half its coefficient (-333.3333334). Square it (111111.1112) and add it to both sides. Add '111111.1112' to each side of the equation. -666.6666667x + 111111.1112 + x2 = -10833.33333 + 111111.1112 Reorder the terms: 111111.1112 + -666.6666667x + x2 = -10833.33333 + 111111.1112 Combine like terms: -10833.33333 + 111111.1112 = 100277.77787 111111.1112 + -666.6666667x + x2 = 100277.77787 Factor a perfect square on the left side: (x + -333.3333334)(x + -333.3333334) = 100277.77787 Calculate the square root of the right side: 316.666666812 Break this problem into two subproblems by setting (x + -333.3333334) equal to 316.666666812 and -316.666666812.Subproblem 1
x + -333.3333334 = 316.666666812 Simplifying x + -333.3333334 = 316.666666812 Reorder the terms: -333.3333334 + x = 316.666666812 Solving -333.3333334 + x = 316.666666812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '333.3333334' to each side of the equation. -333.3333334 + 333.3333334 + x = 316.666666812 + 333.3333334 Combine like terms: -333.3333334 + 333.3333334 = 0.0000000 0.0000000 + x = 316.666666812 + 333.3333334 x = 316.666666812 + 333.3333334 Combine like terms: 316.666666812 + 333.3333334 = 650.000000212 x = 650.000000212 Simplifying x = 650.000000212Subproblem 2
x + -333.3333334 = -316.666666812 Simplifying x + -333.3333334 = -316.666666812 Reorder the terms: -333.3333334 + x = -316.666666812 Solving -333.3333334 + x = -316.666666812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '333.3333334' to each side of the equation. -333.3333334 + 333.3333334 + x = -316.666666812 + 333.3333334 Combine like terms: -333.3333334 + 333.3333334 = 0.0000000 0.0000000 + x = -316.666666812 + 333.3333334 x = -316.666666812 + 333.3333334 Combine like terms: -316.666666812 + 333.3333334 = 16.666666588 x = 16.666666588 Simplifying x = 16.666666588Solution
The solution to the problem is based on the solutions from the subproblems. x = {650.000000212, 16.666666588}
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