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Simplifying 8.8 = 0.0021x2 + -0.286x + 16.28 Reorder the terms: 8.8 = 16.28 + -0.286x + 0.0021x2 Solving 8.8 = 16.28 + -0.286x + 0.0021x2 Solving for variable 'x'. Combine like terms: 8.8 + -16.28 = -7.48 -7.48 + 0.286x + -0.0021x2 = 16.28 + -0.286x + 0.0021x2 + -16.28 + 0.286x + -0.0021x2 Reorder the terms: -7.48 + 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 -7.48 + 0.286x + -0.0021x2 = 0.00 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 -7.48 + 0.286x + -0.0021x2 = -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: -0.286x + 0.286x = 0.000 -7.48 + 0.286x + -0.0021x2 = 0.000 + 0.0021x2 + -0.0021x2 -7.48 + 0.286x + -0.0021x2 = 0.0021x2 + -0.0021x2 Combine like terms: 0.0021x2 + -0.0021x2 = 0.0000 -7.48 + 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'. 3561.904762 + -136.1904762x + x2 = 0 Move the constant term to the right: Add '-3561.904762' to each side of the equation. 3561.904762 + -136.1904762x + -3561.904762 + x2 = 0 + -3561.904762 Reorder the terms: 3561.904762 + -3561.904762 + -136.1904762x + x2 = 0 + -3561.904762 Combine like terms: 3561.904762 + -3561.904762 = 0.000000 0.000000 + -136.1904762x + x2 = 0 + -3561.904762 -136.1904762x + x2 = 0 + -3561.904762 Combine like terms: 0 + -3561.904762 = -3561.904762 -136.1904762x + x2 = -3561.904762 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 = -3561.904762 + 4636.961452 Reorder the terms: 4636.961452 + -136.1904762x + x2 = -3561.904762 + 4636.961452 Combine like terms: -3561.904762 + 4636.961452 = 1075.05669 4636.961452 + -136.1904762x + x2 = 1075.05669 Factor a perfect square on the left side: (x + -68.0952381)(x + -68.0952381) = 1075.05669 Calculate the square root of the right side: 32.788057125 Break this problem into two subproblems by setting (x + -68.0952381) equal to 32.788057125 and -32.788057125.Subproblem 1
x + -68.0952381 = 32.788057125 Simplifying x + -68.0952381 = 32.788057125 Reorder the terms: -68.0952381 + x = 32.788057125 Solving -68.0952381 + x = 32.788057125 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 = 32.788057125 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = 32.788057125 + 68.0952381 x = 32.788057125 + 68.0952381 Combine like terms: 32.788057125 + 68.0952381 = 100.883295225 x = 100.883295225 Simplifying x = 100.883295225Subproblem 2
x + -68.0952381 = -32.788057125 Simplifying x + -68.0952381 = -32.788057125 Reorder the terms: -68.0952381 + x = -32.788057125 Solving -68.0952381 + x = -32.788057125 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 = -32.788057125 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = -32.788057125 + 68.0952381 x = -32.788057125 + 68.0952381 Combine like terms: -32.788057125 + 68.0952381 = 35.307180975 x = 35.307180975 Simplifying x = 35.307180975Solution
The solution to the problem is based on the solutions from the subproblems. x = {100.883295225, 35.307180975}
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