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Simplifying 3x2 + 20x + -15 = 0 Reorder the terms: -15 + 20x + 3x2 = 0 Solving -15 + 20x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5 + 6.666666667x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 6.666666667x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 6.666666667x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 6.666666667x + x2 = 0 + 5 6.666666667x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 6.666666667x + x2 = 5 The x term is 6.666666667x. Take half its coefficient (3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. 6.666666667x + 11.11111112 + x2 = 5 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667x + x2 = 5 + 11.11111112 Combine like terms: 5 + 11.11111112 = 16.11111112 11.11111112 + 6.666666667x + x2 = 16.11111112 Factor a perfect square on the left side: (x + 3.333333334)(x + 3.333333334) = 16.11111112 Calculate the square root of the right side: 4.013864861 Break this problem into two subproblems by setting (x + 3.333333334) equal to 4.013864861 and -4.013864861.Subproblem 1
x + 3.333333334 = 4.013864861 Simplifying x + 3.333333334 = 4.013864861 Reorder the terms: 3.333333334 + x = 4.013864861 Solving 3.333333334 + x = 4.013864861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = 4.013864861 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = 4.013864861 + -3.333333334 x = 4.013864861 + -3.333333334 Combine like terms: 4.013864861 + -3.333333334 = 0.680531527 x = 0.680531527 Simplifying x = 0.680531527Subproblem 2
x + 3.333333334 = -4.013864861 Simplifying x + 3.333333334 = -4.013864861 Reorder the terms: 3.333333334 + x = -4.013864861 Solving 3.333333334 + x = -4.013864861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = -4.013864861 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = -4.013864861 + -3.333333334 x = -4.013864861 + -3.333333334 Combine like terms: -4.013864861 + -3.333333334 = -7.347198195 x = -7.347198195 Simplifying x = -7.347198195Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.680531527, -7.347198195}
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