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Simplifying 1.3x2 = -2.7x + 11.1 Reorder the terms: 1.3x2 = 11.1 + -2.7x Solving 1.3x2 = 11.1 + -2.7x Solving for variable 'x'. Reorder the terms: -11.1 + 2.7x + 1.3x2 = 11.1 + -2.7x + -11.1 + 2.7x Reorder the terms: -11.1 + 2.7x + 1.3x2 = 11.1 + -11.1 + -2.7x + 2.7x Combine like terms: 11.1 + -11.1 = 0.0 -11.1 + 2.7x + 1.3x2 = 0.0 + -2.7x + 2.7x -11.1 + 2.7x + 1.3x2 = -2.7x + 2.7x Combine like terms: -2.7x + 2.7x = 0.0 -11.1 + 2.7x + 1.3x2 = 0.0 Begin completing the square. Divide all terms by 1.3 the coefficient of the squared term: Divide each side by '1.3'. -8.538461538 + 2.076923077x + x2 = 0 Move the constant term to the right: Add '8.538461538' to each side of the equation. -8.538461538 + 2.076923077x + 8.538461538 + x2 = 0 + 8.538461538 Reorder the terms: -8.538461538 + 8.538461538 + 2.076923077x + x2 = 0 + 8.538461538 Combine like terms: -8.538461538 + 8.538461538 = 0.000000000 0.000000000 + 2.076923077x + x2 = 0 + 8.538461538 2.076923077x + x2 = 0 + 8.538461538 Combine like terms: 0 + 8.538461538 = 8.538461538 2.076923077x + x2 = 8.538461538 The x term is 2.076923077x. Take half its coefficient (1.038461539). Square it (1.078402368) and add it to both sides. Add '1.078402368' to each side of the equation. 2.076923077x + 1.078402368 + x2 = 8.538461538 + 1.078402368 Reorder the terms: 1.078402368 + 2.076923077x + x2 = 8.538461538 + 1.078402368 Combine like terms: 8.538461538 + 1.078402368 = 9.616863906 1.078402368 + 2.076923077x + x2 = 9.616863906 Factor a perfect square on the left side: (x + 1.038461539)(x + 1.038461539) = 9.616863906 Calculate the square root of the right side: 3.101106884 Break this problem into two subproblems by setting (x + 1.038461539) equal to 3.101106884 and -3.101106884.Subproblem 1
x + 1.038461539 = 3.101106884 Simplifying x + 1.038461539 = 3.101106884 Reorder the terms: 1.038461539 + x = 3.101106884 Solving 1.038461539 + x = 3.101106884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.038461539' to each side of the equation. 1.038461539 + -1.038461539 + x = 3.101106884 + -1.038461539 Combine like terms: 1.038461539 + -1.038461539 = 0.000000000 0.000000000 + x = 3.101106884 + -1.038461539 x = 3.101106884 + -1.038461539 Combine like terms: 3.101106884 + -1.038461539 = 2.062645345 x = 2.062645345 Simplifying x = 2.062645345Subproblem 2
x + 1.038461539 = -3.101106884 Simplifying x + 1.038461539 = -3.101106884 Reorder the terms: 1.038461539 + x = -3.101106884 Solving 1.038461539 + x = -3.101106884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.038461539' to each side of the equation. 1.038461539 + -1.038461539 + x = -3.101106884 + -1.038461539 Combine like terms: 1.038461539 + -1.038461539 = 0.000000000 0.000000000 + x = -3.101106884 + -1.038461539 x = -3.101106884 + -1.038461539 Combine like terms: -3.101106884 + -1.038461539 = -4.139568423 x = -4.139568423 Simplifying x = -4.139568423Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.062645345, -4.139568423}
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