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Simplifying 4.45x2 + -1200.26x + 26955 = 0 Reorder the terms: 26955 + -1200.26x + 4.45x2 = 0 Solving 26955 + -1200.26x + 4.45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.45 the coefficient of the squared term: Divide each side by '4.45'. 6057.303371 + -269.7213483x + x2 = 0 Move the constant term to the right: Add '-6057.303371' to each side of the equation. 6057.303371 + -269.7213483x + -6057.303371 + x2 = 0 + -6057.303371 Reorder the terms: 6057.303371 + -6057.303371 + -269.7213483x + x2 = 0 + -6057.303371 Combine like terms: 6057.303371 + -6057.303371 = 0.000000 0.000000 + -269.7213483x + x2 = 0 + -6057.303371 -269.7213483x + x2 = 0 + -6057.303371 Combine like terms: 0 + -6057.303371 = -6057.303371 -269.7213483x + x2 = -6057.303371 The x term is -269.7213483x. Take half its coefficient (-134.8606742). Square it (18187.40145) and add it to both sides. Add '18187.40145' to each side of the equation. -269.7213483x + 18187.40145 + x2 = -6057.303371 + 18187.40145 Reorder the terms: 18187.40145 + -269.7213483x + x2 = -6057.303371 + 18187.40145 Combine like terms: -6057.303371 + 18187.40145 = 12130.098079 18187.40145 + -269.7213483x + x2 = 12130.098079 Factor a perfect square on the left side: (x + -134.8606742)(x + -134.8606742) = 12130.098079 Calculate the square root of the right side: 110.136724479 Break this problem into two subproblems by setting (x + -134.8606742) equal to 110.136724479 and -110.136724479.Subproblem 1
x + -134.8606742 = 110.136724479 Simplifying x + -134.8606742 = 110.136724479 Reorder the terms: -134.8606742 + x = 110.136724479 Solving -134.8606742 + x = 110.136724479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '134.8606742' to each side of the equation. -134.8606742 + 134.8606742 + x = 110.136724479 + 134.8606742 Combine like terms: -134.8606742 + 134.8606742 = 0.0000000 0.0000000 + x = 110.136724479 + 134.8606742 x = 110.136724479 + 134.8606742 Combine like terms: 110.136724479 + 134.8606742 = 244.997398679 x = 244.997398679 Simplifying x = 244.997398679Subproblem 2
x + -134.8606742 = -110.136724479 Simplifying x + -134.8606742 = -110.136724479 Reorder the terms: -134.8606742 + x = -110.136724479 Solving -134.8606742 + x = -110.136724479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '134.8606742' to each side of the equation. -134.8606742 + 134.8606742 + x = -110.136724479 + 134.8606742 Combine like terms: -134.8606742 + 134.8606742 = 0.0000000 0.0000000 + x = -110.136724479 + 134.8606742 x = -110.136724479 + 134.8606742 Combine like terms: -110.136724479 + 134.8606742 = 24.723949721 x = 24.723949721 Simplifying x = 24.723949721Solution
The solution to the problem is based on the solutions from the subproblems. x = {244.997398679, 24.723949721}
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