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Simplifying 60 + -2x + -3x2 = 0 Solving 60 + -2x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -20 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 0.6666666667x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 0.6666666667x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 0.6666666667x + x2 = 0 + 20 0.6666666667x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 0.6666666667x + x2 = 20 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 20 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 20 + 0.1111111112 Combine like terms: 20 + 0.1111111112 = 20.1111111112 0.1111111112 + 0.6666666667x + x2 = 20.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 20.1111111112 Calculate the square root of the right side: 4.484541349 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 4.484541349 and -4.484541349.Subproblem 1
x + 0.3333333334 = 4.484541349 Simplifying x + 0.3333333334 = 4.484541349 Reorder the terms: 0.3333333334 + x = 4.484541349 Solving 0.3333333334 + x = 4.484541349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 4.484541349 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 4.484541349 + -0.3333333334 x = 4.484541349 + -0.3333333334 Combine like terms: 4.484541349 + -0.3333333334 = 4.1512080156 x = 4.1512080156 Simplifying x = 4.1512080156Subproblem 2
x + 0.3333333334 = -4.484541349 Simplifying x + 0.3333333334 = -4.484541349 Reorder the terms: 0.3333333334 + x = -4.484541349 Solving 0.3333333334 + x = -4.484541349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -4.484541349 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -4.484541349 + -0.3333333334 x = -4.484541349 + -0.3333333334 Combine like terms: -4.484541349 + -0.3333333334 = -4.8178746824 x = -4.8178746824 Simplifying x = -4.8178746824Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.1512080156, -4.8178746824}
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