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Simplifying 1.15x2 = x2 + -18.44x + 36 Reorder the terms: 1.15x2 = 36 + -18.44x + x2 Solving 1.15x2 = 36 + -18.44x + x2 Solving for variable 'x'. Reorder the terms: -36 + 18.44x + 1.15x2 + -1x2 = 36 + -18.44x + x2 + -36 + 18.44x + -1x2 Combine like terms: 1.15x2 + -1x2 = 0.15x2 -36 + 18.44x + 0.15x2 = 36 + -18.44x + x2 + -36 + 18.44x + -1x2 Reorder the terms: -36 + 18.44x + 0.15x2 = 36 + -36 + -18.44x + 18.44x + x2 + -1x2 Combine like terms: 36 + -36 = 0 -36 + 18.44x + 0.15x2 = 0 + -18.44x + 18.44x + x2 + -1x2 -36 + 18.44x + 0.15x2 = -18.44x + 18.44x + x2 + -1x2 Combine like terms: -18.44x + 18.44x = 0.00 -36 + 18.44x + 0.15x2 = 0.00 + x2 + -1x2 -36 + 18.44x + 0.15x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -36 + 18.44x + 0.15x2 = 0 Begin completing the square. Divide all terms by 0.15 the coefficient of the squared term: Divide each side by '0.15'. -240 + 122.9333333x + x2 = 0 Move the constant term to the right: Add '240' to each side of the equation. -240 + 122.9333333x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + 122.9333333x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 122.9333333x + x2 = 0 + 240 122.9333333x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 122.9333333x + x2 = 240 The x term is 122.9333333x. Take half its coefficient (61.46666665). Square it (3778.151109) and add it to both sides. Add '3778.151109' to each side of the equation. 122.9333333x + 3778.151109 + x2 = 240 + 3778.151109 Reorder the terms: 3778.151109 + 122.9333333x + x2 = 240 + 3778.151109 Combine like terms: 240 + 3778.151109 = 4018.151109 3778.151109 + 122.9333333x + x2 = 4018.151109 Factor a perfect square on the left side: (x + 61.46666665)(x + 61.46666665) = 4018.151109 Calculate the square root of the right side: 63.388887898 Break this problem into two subproblems by setting (x + 61.46666665) equal to 63.388887898 and -63.388887898.Subproblem 1
x + 61.46666665 = 63.388887898 Simplifying x + 61.46666665 = 63.388887898 Reorder the terms: 61.46666665 + x = 63.388887898 Solving 61.46666665 + x = 63.388887898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-61.46666665' to each side of the equation. 61.46666665 + -61.46666665 + x = 63.388887898 + -61.46666665 Combine like terms: 61.46666665 + -61.46666665 = 0.00000000 0.00000000 + x = 63.388887898 + -61.46666665 x = 63.388887898 + -61.46666665 Combine like terms: 63.388887898 + -61.46666665 = 1.922221248 x = 1.922221248 Simplifying x = 1.922221248Subproblem 2
x + 61.46666665 = -63.388887898 Simplifying x + 61.46666665 = -63.388887898 Reorder the terms: 61.46666665 + x = -63.388887898 Solving 61.46666665 + x = -63.388887898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-61.46666665' to each side of the equation. 61.46666665 + -61.46666665 + x = -63.388887898 + -61.46666665 Combine like terms: 61.46666665 + -61.46666665 = 0.00000000 0.00000000 + x = -63.388887898 + -61.46666665 x = -63.388887898 + -61.46666665 Combine like terms: -63.388887898 + -61.46666665 = -124.855554548 x = -124.855554548 Simplifying x = -124.855554548Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.922221248, -124.855554548}
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