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Simplifying 116x2 + -15x = 17 Reorder the terms: -15x + 116x2 = 17 Solving -15x + 116x2 = 17 Solving for variable 'x'. Reorder the terms: -17 + -15x + 116x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + -15x + 116x2 = 0 Begin completing the square. Divide all terms by 116 the coefficient of the squared term: Divide each side by '116'. -0.1465517241 + -0.1293103448x + x2 = 0 Move the constant term to the right: Add '0.1465517241' to each side of the equation. -0.1465517241 + -0.1293103448x + 0.1465517241 + x2 = 0 + 0.1465517241 Reorder the terms: -0.1465517241 + 0.1465517241 + -0.1293103448x + x2 = 0 + 0.1465517241 Combine like terms: -0.1465517241 + 0.1465517241 = 0.0000000000 0.0000000000 + -0.1293103448x + x2 = 0 + 0.1465517241 -0.1293103448x + x2 = 0 + 0.1465517241 Combine like terms: 0 + 0.1465517241 = 0.1465517241 -0.1293103448x + x2 = 0.1465517241 The x term is -0.1293103448x. Take half its coefficient (-0.0646551724). Square it (0.004180291318) and add it to both sides. Add '0.004180291318' to each side of the equation. -0.1293103448x + 0.004180291318 + x2 = 0.1465517241 + 0.004180291318 Reorder the terms: 0.004180291318 + -0.1293103448x + x2 = 0.1465517241 + 0.004180291318 Combine like terms: 0.1465517241 + 0.004180291318 = 0.150732015418 0.004180291318 + -0.1293103448x + x2 = 0.150732015418 Factor a perfect square on the left side: (x + -0.0646551724)(x + -0.0646551724) = 0.150732015418 Calculate the square root of the right side: 0.388242212 Break this problem into two subproblems by setting (x + -0.0646551724) equal to 0.388242212 and -0.388242212.Subproblem 1
x + -0.0646551724 = 0.388242212 Simplifying x + -0.0646551724 = 0.388242212 Reorder the terms: -0.0646551724 + x = 0.388242212 Solving -0.0646551724 + x = 0.388242212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0646551724' to each side of the equation. -0.0646551724 + 0.0646551724 + x = 0.388242212 + 0.0646551724 Combine like terms: -0.0646551724 + 0.0646551724 = 0.0000000000 0.0000000000 + x = 0.388242212 + 0.0646551724 x = 0.388242212 + 0.0646551724 Combine like terms: 0.388242212 + 0.0646551724 = 0.4528973844 x = 0.4528973844 Simplifying x = 0.4528973844Subproblem 2
x + -0.0646551724 = -0.388242212 Simplifying x + -0.0646551724 = -0.388242212 Reorder the terms: -0.0646551724 + x = -0.388242212 Solving -0.0646551724 + x = -0.388242212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0646551724' to each side of the equation. -0.0646551724 + 0.0646551724 + x = -0.388242212 + 0.0646551724 Combine like terms: -0.0646551724 + 0.0646551724 = 0.0000000000 0.0000000000 + x = -0.388242212 + 0.0646551724 x = -0.388242212 + 0.0646551724 Combine like terms: -0.388242212 + 0.0646551724 = -0.3235870396 x = -0.3235870396 Simplifying x = -0.3235870396Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4528973844, -0.3235870396}
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