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Simplifying 57x2 + 20x + -18 = 0 Reorder the terms: -18 + 20x + 57x2 = 0 Solving -18 + 20x + 57x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 57 the coefficient of the squared term: Divide each side by '57'. -0.3157894737 + 0.350877193x + x2 = 0 Move the constant term to the right: Add '0.3157894737' to each side of the equation. -0.3157894737 + 0.350877193x + 0.3157894737 + x2 = 0 + 0.3157894737 Reorder the terms: -0.3157894737 + 0.3157894737 + 0.350877193x + x2 = 0 + 0.3157894737 Combine like terms: -0.3157894737 + 0.3157894737 = 0.0000000000 0.0000000000 + 0.350877193x + x2 = 0 + 0.3157894737 0.350877193x + x2 = 0 + 0.3157894737 Combine like terms: 0 + 0.3157894737 = 0.3157894737 0.350877193x + x2 = 0.3157894737 The x term is 0.350877193x. Take half its coefficient (0.1754385965). Square it (0.03077870114) and add it to both sides. Add '0.03077870114' to each side of the equation. 0.350877193x + 0.03077870114 + x2 = 0.3157894737 + 0.03077870114 Reorder the terms: 0.03077870114 + 0.350877193x + x2 = 0.3157894737 + 0.03077870114 Combine like terms: 0.3157894737 + 0.03077870114 = 0.34656817484 0.03077870114 + 0.350877193x + x2 = 0.34656817484 Factor a perfect square on the left side: (x + 0.1754385965)(x + 0.1754385965) = 0.34656817484 Calculate the square root of the right side: 0.588700412 Break this problem into two subproblems by setting (x + 0.1754385965) equal to 0.588700412 and -0.588700412.Subproblem 1
x + 0.1754385965 = 0.588700412 Simplifying x + 0.1754385965 = 0.588700412 Reorder the terms: 0.1754385965 + x = 0.588700412 Solving 0.1754385965 + x = 0.588700412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1754385965' to each side of the equation. 0.1754385965 + -0.1754385965 + x = 0.588700412 + -0.1754385965 Combine like terms: 0.1754385965 + -0.1754385965 = 0.0000000000 0.0000000000 + x = 0.588700412 + -0.1754385965 x = 0.588700412 + -0.1754385965 Combine like terms: 0.588700412 + -0.1754385965 = 0.4132618155 x = 0.4132618155 Simplifying x = 0.4132618155Subproblem 2
x + 0.1754385965 = -0.588700412 Simplifying x + 0.1754385965 = -0.588700412 Reorder the terms: 0.1754385965 + x = -0.588700412 Solving 0.1754385965 + x = -0.588700412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1754385965' to each side of the equation. 0.1754385965 + -0.1754385965 + x = -0.588700412 + -0.1754385965 Combine like terms: 0.1754385965 + -0.1754385965 = 0.0000000000 0.0000000000 + x = -0.588700412 + -0.1754385965 x = -0.588700412 + -0.1754385965 Combine like terms: -0.588700412 + -0.1754385965 = -0.7641390085 x = -0.7641390085 Simplifying x = -0.7641390085Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4132618155, -0.7641390085}
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