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Simplifying 45 = 0.0021x2 + -0.286x + 16.28 Reorder the terms: 45 = 16.28 + -0.286x + 0.0021x2 Solving 45 = 16.28 + -0.286x + 0.0021x2 Solving for variable 'x'. Combine like terms: 45 + -16.28 = 28.72 28.72 + 0.286x + -0.0021x2 = 16.28 + -0.286x + 0.0021x2 + -16.28 + 0.286x + -0.0021x2 Reorder the terms: 28.72 + 0.286x + -0.0021x2 = 16.28 + -16.28 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: 16.28 + -16.28 = 0.00 28.72 + 0.286x + -0.0021x2 = 0.00 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 28.72 + 0.286x + -0.0021x2 = -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: -0.286x + 0.286x = 0.000 28.72 + 0.286x + -0.0021x2 = 0.000 + 0.0021x2 + -0.0021x2 28.72 + 0.286x + -0.0021x2 = 0.0021x2 + -0.0021x2 Combine like terms: 0.0021x2 + -0.0021x2 = 0.0000 28.72 + 0.286x + -0.0021x2 = 0.0000 Begin completing the square. Divide all terms by -0.0021 the coefficient of the squared term: Divide each side by '-0.0021'. -13676.19048 + -136.1904762x + x2 = 0 Move the constant term to the right: Add '13676.19048' to each side of the equation. -13676.19048 + -136.1904762x + 13676.19048 + x2 = 0 + 13676.19048 Reorder the terms: -13676.19048 + 13676.19048 + -136.1904762x + x2 = 0 + 13676.19048 Combine like terms: -13676.19048 + 13676.19048 = 0.00000 0.00000 + -136.1904762x + x2 = 0 + 13676.19048 -136.1904762x + x2 = 0 + 13676.19048 Combine like terms: 0 + 13676.19048 = 13676.19048 -136.1904762x + x2 = 13676.19048 The x term is -136.1904762x. Take half its coefficient (-68.0952381). Square it (4636.961452) and add it to both sides. Add '4636.961452' to each side of the equation. -136.1904762x + 4636.961452 + x2 = 13676.19048 + 4636.961452 Reorder the terms: 4636.961452 + -136.1904762x + x2 = 13676.19048 + 4636.961452 Combine like terms: 13676.19048 + 4636.961452 = 18313.151932 4636.961452 + -136.1904762x + x2 = 18313.151932 Factor a perfect square on the left side: (x + -68.0952381)(x + -68.0952381) = 18313.151932 Calculate the square root of the right side: 135.326094793 Break this problem into two subproblems by setting (x + -68.0952381) equal to 135.326094793 and -135.326094793.Subproblem 1
x + -68.0952381 = 135.326094793 Simplifying x + -68.0952381 = 135.326094793 Reorder the terms: -68.0952381 + x = 135.326094793 Solving -68.0952381 + x = 135.326094793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '68.0952381' to each side of the equation. -68.0952381 + 68.0952381 + x = 135.326094793 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = 135.326094793 + 68.0952381 x = 135.326094793 + 68.0952381 Combine like terms: 135.326094793 + 68.0952381 = 203.421332893 x = 203.421332893 Simplifying x = 203.421332893Subproblem 2
x + -68.0952381 = -135.326094793 Simplifying x + -68.0952381 = -135.326094793 Reorder the terms: -68.0952381 + x = -135.326094793 Solving -68.0952381 + x = -135.326094793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '68.0952381' to each side of the equation. -68.0952381 + 68.0952381 + x = -135.326094793 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = -135.326094793 + 68.0952381 x = -135.326094793 + 68.0952381 Combine like terms: -135.326094793 + 68.0952381 = -67.230856693 x = -67.230856693 Simplifying x = -67.230856693Solution
The solution to the problem is based on the solutions from the subproblems. x = {203.421332893, -67.230856693}
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