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Simplifying -3x2 + 20x + 12 = 0 Reorder the terms: 12 + 20x + -3x2 = 0 Solving 12 + 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'. -4 + -6.666666667x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -6.666666667x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -6.666666667x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -6.666666667x + x2 = 0 + 4 -6.666666667x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -6.666666667x + x2 = 4 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 = 4 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667x + x2 = 4 + 11.11111112 Combine like terms: 4 + 11.11111112 = 15.11111112 11.11111112 + -6.666666667x + x2 = 15.11111112 Factor a perfect square on the left side: (x + -3.333333334)(x + -3.333333334) = 15.11111112 Calculate the square root of the right side: 3.887301264 Break this problem into two subproblems by setting (x + -3.333333334) equal to 3.887301264 and -3.887301264.Subproblem 1
x + -3.333333334 = 3.887301264 Simplifying x + -3.333333334 = 3.887301264 Reorder the terms: -3.333333334 + x = 3.887301264 Solving -3.333333334 + x = 3.887301264 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 = 3.887301264 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = 3.887301264 + 3.333333334 x = 3.887301264 + 3.333333334 Combine like terms: 3.887301264 + 3.333333334 = 7.220634598 x = 7.220634598 Simplifying x = 7.220634598Subproblem 2
x + -3.333333334 = -3.887301264 Simplifying x + -3.333333334 = -3.887301264 Reorder the terms: -3.333333334 + x = -3.887301264 Solving -3.333333334 + x = -3.887301264 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 = -3.887301264 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = -3.887301264 + 3.333333334 x = -3.887301264 + 3.333333334 Combine like terms: -3.887301264 + 3.333333334 = -0.55396793 x = -0.55396793 Simplifying x = -0.55396793Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.220634598, -0.55396793}
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