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Simplifying 3.14x2 + 9 + -90x = 0 Reorder the terms: 9 + -90x + 3.14x2 = 0 Solving 9 + -90x + 3.14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.14 the coefficient of the squared term: Divide each side by '3.14'. 2.866242038 + -28.66242038x + x2 = 0 Move the constant term to the right: Add '-2.866242038' to each side of the equation. 2.866242038 + -28.66242038x + -2.866242038 + x2 = 0 + -2.866242038 Reorder the terms: 2.866242038 + -2.866242038 + -28.66242038x + x2 = 0 + -2.866242038 Combine like terms: 2.866242038 + -2.866242038 = 0.000000000 0.000000000 + -28.66242038x + x2 = 0 + -2.866242038 -28.66242038x + x2 = 0 + -2.866242038 Combine like terms: 0 + -2.866242038 = -2.866242038 -28.66242038x + x2 = -2.866242038 The x term is -28.66242038x. Take half its coefficient (-14.33121019). Square it (205.3835855) and add it to both sides. Add '205.3835855' to each side of the equation. -28.66242038x + 205.3835855 + x2 = -2.866242038 + 205.3835855 Reorder the terms: 205.3835855 + -28.66242038x + x2 = -2.866242038 + 205.3835855 Combine like terms: -2.866242038 + 205.3835855 = 202.517343462 205.3835855 + -28.66242038x + x2 = 202.517343462 Factor a perfect square on the left side: (x + -14.33121019)(x + -14.33121019) = 202.517343462 Calculate the square root of the right side: 14.230858845 Break this problem into two subproblems by setting (x + -14.33121019) equal to 14.230858845 and -14.230858845.Subproblem 1
x + -14.33121019 = 14.230858845 Simplifying x + -14.33121019 = 14.230858845 Reorder the terms: -14.33121019 + x = 14.230858845 Solving -14.33121019 + x = 14.230858845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.33121019' to each side of the equation. -14.33121019 + 14.33121019 + x = 14.230858845 + 14.33121019 Combine like terms: -14.33121019 + 14.33121019 = 0.00000000 0.00000000 + x = 14.230858845 + 14.33121019 x = 14.230858845 + 14.33121019 Combine like terms: 14.230858845 + 14.33121019 = 28.562069035 x = 28.562069035 Simplifying x = 28.562069035Subproblem 2
x + -14.33121019 = -14.230858845 Simplifying x + -14.33121019 = -14.230858845 Reorder the terms: -14.33121019 + x = -14.230858845 Solving -14.33121019 + x = -14.230858845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.33121019' to each side of the equation. -14.33121019 + 14.33121019 + x = -14.230858845 + 14.33121019 Combine like terms: -14.33121019 + 14.33121019 = 0.00000000 0.00000000 + x = -14.230858845 + 14.33121019 x = -14.230858845 + 14.33121019 Combine like terms: -14.230858845 + 14.33121019 = 0.100351345 x = 0.100351345 Simplifying x = 0.100351345Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.562069035, 0.100351345}
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