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Simplifying 4.905x2 + -58.9x + 117.8 = 0 Reorder the terms: 117.8 + -58.9x + 4.905x2 = 0 Solving 117.8 + -58.9x + 4.905x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. 24.01630989 + -12.00815494x + x2 = 0 Move the constant term to the right: Add '-24.01630989' to each side of the equation. 24.01630989 + -12.00815494x + -24.01630989 + x2 = 0 + -24.01630989 Reorder the terms: 24.01630989 + -24.01630989 + -12.00815494x + x2 = 0 + -24.01630989 Combine like terms: 24.01630989 + -24.01630989 = 0.00000000 0.00000000 + -12.00815494x + x2 = 0 + -24.01630989 -12.00815494x + x2 = 0 + -24.01630989 Combine like terms: 0 + -24.01630989 = -24.01630989 -12.00815494x + x2 = -24.01630989 The x term is -12.00815494x. Take half its coefficient (-6.00407747). Square it (36.04894627) and add it to both sides. Add '36.04894627' to each side of the equation. -12.00815494x + 36.04894627 + x2 = -24.01630989 + 36.04894627 Reorder the terms: 36.04894627 + -12.00815494x + x2 = -24.01630989 + 36.04894627 Combine like terms: -24.01630989 + 36.04894627 = 12.03263638 36.04894627 + -12.00815494x + x2 = 12.03263638 Factor a perfect square on the left side: (x + -6.00407747)(x + -6.00407747) = 12.03263638 Calculate the square root of the right side: 3.468809072 Break this problem into two subproblems by setting (x + -6.00407747) equal to 3.468809072 and -3.468809072.Subproblem 1
x + -6.00407747 = 3.468809072 Simplifying x + -6.00407747 = 3.468809072 Reorder the terms: -6.00407747 + x = 3.468809072 Solving -6.00407747 + x = 3.468809072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.00407747' to each side of the equation. -6.00407747 + 6.00407747 + x = 3.468809072 + 6.00407747 Combine like terms: -6.00407747 + 6.00407747 = 0.00000000 0.00000000 + x = 3.468809072 + 6.00407747 x = 3.468809072 + 6.00407747 Combine like terms: 3.468809072 + 6.00407747 = 9.472886542 x = 9.472886542 Simplifying x = 9.472886542Subproblem 2
x + -6.00407747 = -3.468809072 Simplifying x + -6.00407747 = -3.468809072 Reorder the terms: -6.00407747 + x = -3.468809072 Solving -6.00407747 + x = -3.468809072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.00407747' to each side of the equation. -6.00407747 + 6.00407747 + x = -3.468809072 + 6.00407747 Combine like terms: -6.00407747 + 6.00407747 = 0.00000000 0.00000000 + x = -3.468809072 + 6.00407747 x = -3.468809072 + 6.00407747 Combine like terms: -3.468809072 + 6.00407747 = 2.535268398 x = 2.535268398 Simplifying x = 2.535268398Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.472886542, 2.535268398}
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