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Simplifying 13x2 + 70x + -30 = 0 Reorder the terms: -30 + 70x + 13x2 = 0 Solving -30 + 70x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -2.307692308 + 5.384615385x + x2 = 0 Move the constant term to the right: Add '2.307692308' to each side of the equation. -2.307692308 + 5.384615385x + 2.307692308 + x2 = 0 + 2.307692308 Reorder the terms: -2.307692308 + 2.307692308 + 5.384615385x + x2 = 0 + 2.307692308 Combine like terms: -2.307692308 + 2.307692308 = 0.000000000 0.000000000 + 5.384615385x + x2 = 0 + 2.307692308 5.384615385x + x2 = 0 + 2.307692308 Combine like terms: 0 + 2.307692308 = 2.307692308 5.384615385x + x2 = 2.307692308 The x term is 5.384615385x. Take half its coefficient (2.692307693). Square it (7.248520714) and add it to both sides. Add '7.248520714' to each side of the equation. 5.384615385x + 7.248520714 + x2 = 2.307692308 + 7.248520714 Reorder the terms: 7.248520714 + 5.384615385x + x2 = 2.307692308 + 7.248520714 Combine like terms: 2.307692308 + 7.248520714 = 9.556213022 7.248520714 + 5.384615385x + x2 = 9.556213022 Factor a perfect square on the left side: (x + 2.692307693)(x + 2.692307693) = 9.556213022 Calculate the square root of the right side: 3.091312508 Break this problem into two subproblems by setting (x + 2.692307693) equal to 3.091312508 and -3.091312508.Subproblem 1
x + 2.692307693 = 3.091312508 Simplifying x + 2.692307693 = 3.091312508 Reorder the terms: 2.692307693 + x = 3.091312508 Solving 2.692307693 + x = 3.091312508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.692307693' to each side of the equation. 2.692307693 + -2.692307693 + x = 3.091312508 + -2.692307693 Combine like terms: 2.692307693 + -2.692307693 = 0.000000000 0.000000000 + x = 3.091312508 + -2.692307693 x = 3.091312508 + -2.692307693 Combine like terms: 3.091312508 + -2.692307693 = 0.399004815 x = 0.399004815 Simplifying x = 0.399004815Subproblem 2
x + 2.692307693 = -3.091312508 Simplifying x + 2.692307693 = -3.091312508 Reorder the terms: 2.692307693 + x = -3.091312508 Solving 2.692307693 + x = -3.091312508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.692307693' to each side of the equation. 2.692307693 + -2.692307693 + x = -3.091312508 + -2.692307693 Combine like terms: 2.692307693 + -2.692307693 = 0.000000000 0.000000000 + x = -3.091312508 + -2.692307693 x = -3.091312508 + -2.692307693 Combine like terms: -3.091312508 + -2.692307693 = -5.783620201 x = -5.783620201 Simplifying x = -5.783620201Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.399004815, -5.783620201}
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