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Simplifying 15 = 0.0021x2 + -0.286x + 16.28 Reorder the terms: 15 = 16.28 + -0.286x + 0.0021x2 Solving 15 = 16.28 + -0.286x + 0.0021x2 Solving for variable 'x'. Combine like terms: 15 + -16.28 = -1.28 -1.28 + 0.286x + -0.0021x2 = 16.28 + -0.286x + 0.0021x2 + -16.28 + 0.286x + -0.0021x2 Reorder the terms: -1.28 + 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 -1.28 + 0.286x + -0.0021x2 = 0.00 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 -1.28 + 0.286x + -0.0021x2 = -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: -0.286x + 0.286x = 0.000 -1.28 + 0.286x + -0.0021x2 = 0.000 + 0.0021x2 + -0.0021x2 -1.28 + 0.286x + -0.0021x2 = 0.0021x2 + -0.0021x2 Combine like terms: 0.0021x2 + -0.0021x2 = 0.0000 -1.28 + 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'. 609.5238095 + -136.1904762x + x2 = 0 Move the constant term to the right: Add '-609.5238095' to each side of the equation. 609.5238095 + -136.1904762x + -609.5238095 + x2 = 0 + -609.5238095 Reorder the terms: 609.5238095 + -609.5238095 + -136.1904762x + x2 = 0 + -609.5238095 Combine like terms: 609.5238095 + -609.5238095 = 0.0000000 0.0000000 + -136.1904762x + x2 = 0 + -609.5238095 -136.1904762x + x2 = 0 + -609.5238095 Combine like terms: 0 + -609.5238095 = -609.5238095 -136.1904762x + x2 = -609.5238095 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 = -609.5238095 + 4636.961452 Reorder the terms: 4636.961452 + -136.1904762x + x2 = -609.5238095 + 4636.961452 Combine like terms: -609.5238095 + 4636.961452 = 4027.4376425 4636.961452 + -136.1904762x + x2 = 4027.4376425 Factor a perfect square on the left side: (x + -68.0952381)(x + -68.0952381) = 4027.4376425 Calculate the square root of the right side: 63.462096109 Break this problem into two subproblems by setting (x + -68.0952381) equal to 63.462096109 and -63.462096109.Subproblem 1
x + -68.0952381 = 63.462096109 Simplifying x + -68.0952381 = 63.462096109 Reorder the terms: -68.0952381 + x = 63.462096109 Solving -68.0952381 + x = 63.462096109 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 = 63.462096109 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = 63.462096109 + 68.0952381 x = 63.462096109 + 68.0952381 Combine like terms: 63.462096109 + 68.0952381 = 131.557334209 x = 131.557334209 Simplifying x = 131.557334209Subproblem 2
x + -68.0952381 = -63.462096109 Simplifying x + -68.0952381 = -63.462096109 Reorder the terms: -68.0952381 + x = -63.462096109 Solving -68.0952381 + x = -63.462096109 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 = -63.462096109 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = -63.462096109 + 68.0952381 x = -63.462096109 + 68.0952381 Combine like terms: -63.462096109 + 68.0952381 = 4.633141991 x = 4.633141991 Simplifying x = 4.633141991Solution
The solution to the problem is based on the solutions from the subproblems. x = {131.557334209, 4.633141991}
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