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Simplifying -3x2 + 14x + -9 = 0 Reorder the terms: -9 + 14x + -3x2 = 0 Solving -9 + 14x + -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'. 3 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -4.666666667x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -4.666666667x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4.666666667x + x2 = 0 + -3 -4.666666667x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4.666666667x + x2 = -3 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = -3 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = -3 + 5.444444448 Combine like terms: -3 + 5.444444448 = 2.444444448 5.444444448 + -4.666666667x + x2 = 2.444444448 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 2.444444448 Calculate the square root of the right side: 1.563471921 Break this problem into two subproblems by setting (x + -2.333333334) equal to 1.563471921 and -1.563471921.Subproblem 1
x + -2.333333334 = 1.563471921 Simplifying x + -2.333333334 = 1.563471921 Reorder the terms: -2.333333334 + x = 1.563471921 Solving -2.333333334 + x = 1.563471921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 1.563471921 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 1.563471921 + 2.333333334 x = 1.563471921 + 2.333333334 Combine like terms: 1.563471921 + 2.333333334 = 3.896805255 x = 3.896805255 Simplifying x = 3.896805255Subproblem 2
x + -2.333333334 = -1.563471921 Simplifying x + -2.333333334 = -1.563471921 Reorder the terms: -2.333333334 + x = -1.563471921 Solving -2.333333334 + x = -1.563471921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -1.563471921 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -1.563471921 + 2.333333334 x = -1.563471921 + 2.333333334 Combine like terms: -1.563471921 + 2.333333334 = 0.769861413 x = 0.769861413 Simplifying x = 0.769861413Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.896805255, 0.769861413}
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