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Simplifying 81x2 + 37x + -15 = 0 Reorder the terms: -15 + 37x + 81x2 = 0 Solving -15 + 37x + 81x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.1851851852 + 0.4567901235x + x2 = 0 Move the constant term to the right: Add '0.1851851852' to each side of the equation. -0.1851851852 + 0.4567901235x + 0.1851851852 + x2 = 0 + 0.1851851852 Reorder the terms: -0.1851851852 + 0.1851851852 + 0.4567901235x + x2 = 0 + 0.1851851852 Combine like terms: -0.1851851852 + 0.1851851852 = 0.0000000000 0.0000000000 + 0.4567901235x + x2 = 0 + 0.1851851852 0.4567901235x + x2 = 0 + 0.1851851852 Combine like terms: 0 + 0.1851851852 = 0.1851851852 0.4567901235x + x2 = 0.1851851852 The x term is 0.4567901235x. Take half its coefficient (0.2283950618). Square it (0.05216430425) and add it to both sides. Add '0.05216430425' to each side of the equation. 0.4567901235x + 0.05216430425 + x2 = 0.1851851852 + 0.05216430425 Reorder the terms: 0.05216430425 + 0.4567901235x + x2 = 0.1851851852 + 0.05216430425 Combine like terms: 0.1851851852 + 0.05216430425 = 0.23734948945 0.05216430425 + 0.4567901235x + x2 = 0.23734948945 Factor a perfect square on the left side: (x + 0.2283950618)(x + 0.2283950618) = 0.23734948945 Calculate the square root of the right side: 0.487185272 Break this problem into two subproblems by setting (x + 0.2283950618) equal to 0.487185272 and -0.487185272.Subproblem 1
x + 0.2283950618 = 0.487185272 Simplifying x + 0.2283950618 = 0.487185272 Reorder the terms: 0.2283950618 + x = 0.487185272 Solving 0.2283950618 + x = 0.487185272 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2283950618' to each side of the equation. 0.2283950618 + -0.2283950618 + x = 0.487185272 + -0.2283950618 Combine like terms: 0.2283950618 + -0.2283950618 = 0.0000000000 0.0000000000 + x = 0.487185272 + -0.2283950618 x = 0.487185272 + -0.2283950618 Combine like terms: 0.487185272 + -0.2283950618 = 0.2587902102 x = 0.2587902102 Simplifying x = 0.2587902102Subproblem 2
x + 0.2283950618 = -0.487185272 Simplifying x + 0.2283950618 = -0.487185272 Reorder the terms: 0.2283950618 + x = -0.487185272 Solving 0.2283950618 + x = -0.487185272 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2283950618' to each side of the equation. 0.2283950618 + -0.2283950618 + x = -0.487185272 + -0.2283950618 Combine like terms: 0.2283950618 + -0.2283950618 = 0.0000000000 0.0000000000 + x = -0.487185272 + -0.2283950618 x = -0.487185272 + -0.2283950618 Combine like terms: -0.487185272 + -0.2283950618 = -0.7155803338 x = -0.7155803338 Simplifying x = -0.7155803338Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2587902102, -0.7155803338}
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