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Simplifying 51x + 81x2 = -1 Solving 51x + 81x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + 51x + 81x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 51x + 81x2 = 0 Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. 0.01234567901 + 0.6296296296x + x2 = 0 Move the constant term to the right: Add '-0.01234567901' to each side of the equation. 0.01234567901 + 0.6296296296x + -0.01234567901 + x2 = 0 + -0.01234567901 Reorder the terms: 0.01234567901 + -0.01234567901 + 0.6296296296x + x2 = 0 + -0.01234567901 Combine like terms: 0.01234567901 + -0.01234567901 = 0.00000000000 0.00000000000 + 0.6296296296x + x2 = 0 + -0.01234567901 0.6296296296x + x2 = 0 + -0.01234567901 Combine like terms: 0 + -0.01234567901 = -0.01234567901 0.6296296296x + x2 = -0.01234567901 The x term is 0.6296296296x. Take half its coefficient (0.3148148148). Square it (0.09910836762) and add it to both sides. Add '0.09910836762' to each side of the equation. 0.6296296296x + 0.09910836762 + x2 = -0.01234567901 + 0.09910836762 Reorder the terms: 0.09910836762 + 0.6296296296x + x2 = -0.01234567901 + 0.09910836762 Combine like terms: -0.01234567901 + 0.09910836762 = 0.08676268861 0.09910836762 + 0.6296296296x + x2 = 0.08676268861 Factor a perfect square on the left side: (x + 0.3148148148)(x + 0.3148148148) = 0.08676268861 Calculate the square root of the right side: 0.294555069 Break this problem into two subproblems by setting (x + 0.3148148148) equal to 0.294555069 and -0.294555069.Subproblem 1
x + 0.3148148148 = 0.294555069 Simplifying x + 0.3148148148 = 0.294555069 Reorder the terms: 0.3148148148 + x = 0.294555069 Solving 0.3148148148 + x = 0.294555069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3148148148' to each side of the equation. 0.3148148148 + -0.3148148148 + x = 0.294555069 + -0.3148148148 Combine like terms: 0.3148148148 + -0.3148148148 = 0.0000000000 0.0000000000 + x = 0.294555069 + -0.3148148148 x = 0.294555069 + -0.3148148148 Combine like terms: 0.294555069 + -0.3148148148 = -0.0202597458 x = -0.0202597458 Simplifying x = -0.0202597458Subproblem 2
x + 0.3148148148 = -0.294555069 Simplifying x + 0.3148148148 = -0.294555069 Reorder the terms: 0.3148148148 + x = -0.294555069 Solving 0.3148148148 + x = -0.294555069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3148148148' to each side of the equation. 0.3148148148 + -0.3148148148 + x = -0.294555069 + -0.3148148148 Combine like terms: 0.3148148148 + -0.3148148148 = 0.0000000000 0.0000000000 + x = -0.294555069 + -0.3148148148 x = -0.294555069 + -0.3148148148 Combine like terms: -0.294555069 + -0.3148148148 = -0.6093698838 x = -0.6093698838 Simplifying x = -0.6093698838Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0202597458, -0.6093698838}
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