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Simplifying 21x2 + 14x + -40 = 0 Reorder the terms: -40 + 14x + 21x2 = 0 Solving -40 + 14x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -1.904761905 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '1.904761905' to each side of the equation. -1.904761905 + 0.6666666667x + 1.904761905 + x2 = 0 + 1.904761905 Reorder the terms: -1.904761905 + 1.904761905 + 0.6666666667x + x2 = 0 + 1.904761905 Combine like terms: -1.904761905 + 1.904761905 = 0.000000000 0.000000000 + 0.6666666667x + x2 = 0 + 1.904761905 0.6666666667x + x2 = 0 + 1.904761905 Combine like terms: 0 + 1.904761905 = 1.904761905 0.6666666667x + x2 = 1.904761905 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 1.904761905 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 1.904761905 + 0.1111111112 Combine like terms: 1.904761905 + 0.1111111112 = 2.0158730162 0.1111111112 + 0.6666666667x + x2 = 2.0158730162 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 2.0158730162 Calculate the square root of the right side: 1.41981443 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 1.41981443 and -1.41981443.Subproblem 1
x + 0.3333333334 = 1.41981443 Simplifying x + 0.3333333334 = 1.41981443 Reorder the terms: 0.3333333334 + x = 1.41981443 Solving 0.3333333334 + x = 1.41981443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 1.41981443 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 1.41981443 + -0.3333333334 x = 1.41981443 + -0.3333333334 Combine like terms: 1.41981443 + -0.3333333334 = 1.0864810966 x = 1.0864810966 Simplifying x = 1.0864810966Subproblem 2
x + 0.3333333334 = -1.41981443 Simplifying x + 0.3333333334 = -1.41981443 Reorder the terms: 0.3333333334 + x = -1.41981443 Solving 0.3333333334 + x = -1.41981443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -1.41981443 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -1.41981443 + -0.3333333334 x = -1.41981443 + -0.3333333334 Combine like terms: -1.41981443 + -0.3333333334 = -1.7531477634 x = -1.7531477634 Simplifying x = -1.7531477634Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0864810966, -1.7531477634}
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