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Simplifying 1 = 117x + -0.563x2 Solving 1 = 117x + -0.563x2 Solving for variable 'x'. Reorder the terms: 1 + -117x + 0.563x2 = 117x + -117x + -0.563x2 + 0.563x2 Combine like terms: 117x + -117x = 0 1 + -117x + 0.563x2 = 0 + -0.563x2 + 0.563x2 1 + -117x + 0.563x2 = -0.563x2 + 0.563x2 Combine like terms: -0.563x2 + 0.563x2 = 0.000 1 + -117x + 0.563x2 = 0.000 Begin completing the square. Divide all terms by 0.563 the coefficient of the squared term: Divide each side by '0.563'. 1.776198934 + -207.8152753x + x2 = 0 Move the constant term to the right: Add '-1.776198934' to each side of the equation. 1.776198934 + -207.8152753x + -1.776198934 + x2 = 0 + -1.776198934 Reorder the terms: 1.776198934 + -1.776198934 + -207.8152753x + x2 = 0 + -1.776198934 Combine like terms: 1.776198934 + -1.776198934 = 0.000000000 0.000000000 + -207.8152753x + x2 = 0 + -1.776198934 -207.8152753x + x2 = 0 + -1.776198934 Combine like terms: 0 + -1.776198934 = -1.776198934 -207.8152753x + x2 = -1.776198934 The x term is -207.8152753x. Take half its coefficient (-103.9076377). Square it (10796.79717) and add it to both sides. Add '10796.79717' to each side of the equation. -207.8152753x + 10796.79717 + x2 = -1.776198934 + 10796.79717 Reorder the terms: 10796.79717 + -207.8152753x + x2 = -1.776198934 + 10796.79717 Combine like terms: -1.776198934 + 10796.79717 = 10795.020971066 10796.79717 + -207.8152753x + x2 = 10795.020971066 Factor a perfect square on the left side: (x + -103.9076377)(x + -103.9076377) = 10795.020971066 Calculate the square root of the right side: 103.899090328 Break this problem into two subproblems by setting (x + -103.9076377) equal to 103.899090328 and -103.899090328.Subproblem 1
x + -103.9076377 = 103.899090328 Simplifying x + -103.9076377 = 103.899090328 Reorder the terms: -103.9076377 + x = 103.899090328 Solving -103.9076377 + x = 103.899090328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '103.9076377' to each side of the equation. -103.9076377 + 103.9076377 + x = 103.899090328 + 103.9076377 Combine like terms: -103.9076377 + 103.9076377 = 0.0000000 0.0000000 + x = 103.899090328 + 103.9076377 x = 103.899090328 + 103.9076377 Combine like terms: 103.899090328 + 103.9076377 = 207.806728028 x = 207.806728028 Simplifying x = 207.806728028Subproblem 2
x + -103.9076377 = -103.899090328 Simplifying x + -103.9076377 = -103.899090328 Reorder the terms: -103.9076377 + x = -103.899090328 Solving -103.9076377 + x = -103.899090328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '103.9076377' to each side of the equation. -103.9076377 + 103.9076377 + x = -103.899090328 + 103.9076377 Combine like terms: -103.9076377 + 103.9076377 = 0.0000000 0.0000000 + x = -103.899090328 + 103.9076377 x = -103.899090328 + 103.9076377 Combine like terms: -103.899090328 + 103.9076377 = 0.008547372 x = 0.008547372 Simplifying x = 0.008547372Solution
The solution to the problem is based on the solutions from the subproblems. x = {207.806728028, 0.008547372}
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