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Simplifying 9x2 + 42x + 49 = 22 Reorder the terms: 49 + 42x + 9x2 = 22 Solving 49 + 42x + 9x2 = 22 Solving for variable 'x'. Reorder the terms: 49 + -22 + 42x + 9x2 = 22 + -22 Combine like terms: 49 + -22 = 27 27 + 42x + 9x2 = 22 + -22 Combine like terms: 22 + -22 = 0 27 + 42x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(9 + 14x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(9 + 14x + 3x2)' equal to zero and attempt to solve: Simplifying 9 + 14x + 3x2 = 0 Solving 9 + 14x + 3x2 = 0 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 = -0.769861413 x = -0.769861413 Simplifying x = -0.769861413Subproblem 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 = -3.896805255 x = -3.896805255 Simplifying x = -3.896805255Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.769861413, -3.896805255}Solution
x = {-0.769861413, -3.896805255}
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