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Simplifying 300 = 1.55x2 + -5.1x + 197 Reorder the terms: 300 = 197 + -5.1x + 1.55x2 Solving 300 = 197 + -5.1x + 1.55x2 Solving for variable 'x'. Combine like terms: 300 + -197 = 103 103 + 5.1x + -1.55x2 = 197 + -5.1x + 1.55x2 + -197 + 5.1x + -1.55x2 Reorder the terms: 103 + 5.1x + -1.55x2 = 197 + -197 + -5.1x + 5.1x + 1.55x2 + -1.55x2 Combine like terms: 197 + -197 = 0 103 + 5.1x + -1.55x2 = 0 + -5.1x + 5.1x + 1.55x2 + -1.55x2 103 + 5.1x + -1.55x2 = -5.1x + 5.1x + 1.55x2 + -1.55x2 Combine like terms: -5.1x + 5.1x = 0.0 103 + 5.1x + -1.55x2 = 0.0 + 1.55x2 + -1.55x2 103 + 5.1x + -1.55x2 = 1.55x2 + -1.55x2 Combine like terms: 1.55x2 + -1.55x2 = 0.00 103 + 5.1x + -1.55x2 = 0.00 Begin completing the square. Divide all terms by -1.55 the coefficient of the squared term: Divide each side by '-1.55'. -66.4516129 + -3.290322581x + x2 = 0 Move the constant term to the right: Add '66.4516129' to each side of the equation. -66.4516129 + -3.290322581x + 66.4516129 + x2 = 0 + 66.4516129 Reorder the terms: -66.4516129 + 66.4516129 + -3.290322581x + x2 = 0 + 66.4516129 Combine like terms: -66.4516129 + 66.4516129 = 0.0000000 0.0000000 + -3.290322581x + x2 = 0 + 66.4516129 -3.290322581x + x2 = 0 + 66.4516129 Combine like terms: 0 + 66.4516129 = 66.4516129 -3.290322581x + x2 = 66.4516129 The x term is -3.290322581x. Take half its coefficient (-1.645161291). Square it (2.706555673) and add it to both sides. Add '2.706555673' to each side of the equation. -3.290322581x + 2.706555673 + x2 = 66.4516129 + 2.706555673 Reorder the terms: 2.706555673 + -3.290322581x + x2 = 66.4516129 + 2.706555673 Combine like terms: 66.4516129 + 2.706555673 = 69.158168573 2.706555673 + -3.290322581x + x2 = 69.158168573 Factor a perfect square on the left side: (x + -1.645161291)(x + -1.645161291) = 69.158168573 Calculate the square root of the right side: 8.316139042 Break this problem into two subproblems by setting (x + -1.645161291) equal to 8.316139042 and -8.316139042.Subproblem 1
x + -1.645161291 = 8.316139042 Simplifying x + -1.645161291 = 8.316139042 Reorder the terms: -1.645161291 + x = 8.316139042 Solving -1.645161291 + x = 8.316139042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.645161291' to each side of the equation. -1.645161291 + 1.645161291 + x = 8.316139042 + 1.645161291 Combine like terms: -1.645161291 + 1.645161291 = 0.000000000 0.000000000 + x = 8.316139042 + 1.645161291 x = 8.316139042 + 1.645161291 Combine like terms: 8.316139042 + 1.645161291 = 9.961300333 x = 9.961300333 Simplifying x = 9.961300333Subproblem 2
x + -1.645161291 = -8.316139042 Simplifying x + -1.645161291 = -8.316139042 Reorder the terms: -1.645161291 + x = -8.316139042 Solving -1.645161291 + x = -8.316139042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.645161291' to each side of the equation. -1.645161291 + 1.645161291 + x = -8.316139042 + 1.645161291 Combine like terms: -1.645161291 + 1.645161291 = 0.000000000 0.000000000 + x = -8.316139042 + 1.645161291 x = -8.316139042 + 1.645161291 Combine like terms: -8.316139042 + 1.645161291 = -6.670977751 x = -6.670977751 Simplifying x = -6.670977751Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.961300333, -6.670977751}
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