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Simplifying 169 = 2x2 + 4x2 + -28x + 49 Reorder the terms: 169 = 49 + -28x + 2x2 + 4x2 Combine like terms: 2x2 + 4x2 = 6x2 169 = 49 + -28x + 6x2 Solving 169 = 49 + -28x + 6x2 Solving for variable 'x'. Combine like terms: 169 + -49 = 120 120 + 28x + -6x2 = 49 + -28x + 6x2 + -49 + 28x + -6x2 Reorder the terms: 120 + 28x + -6x2 = 49 + -49 + -28x + 28x + 6x2 + -6x2 Combine like terms: 49 + -49 = 0 120 + 28x + -6x2 = 0 + -28x + 28x + 6x2 + -6x2 120 + 28x + -6x2 = -28x + 28x + 6x2 + -6x2 Combine like terms: -28x + 28x = 0 120 + 28x + -6x2 = 0 + 6x2 + -6x2 120 + 28x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 120 + 28x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(60 + 14x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(60 + 14x + -3x2)' equal to zero and attempt to solve: Simplifying 60 + 14x + -3x2 = 0 Solving 60 + 14x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -20 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -4.666666667x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -4.666666667x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -4.666666667x + x2 = 0 + 20 -4.666666667x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -4.666666667x + x2 = 20 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 = 20 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = 20 + 5.444444448 Combine like terms: 20 + 5.444444448 = 25.444444448 5.444444448 + -4.666666667x + x2 = 25.444444448 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 25.444444448 Calculate the square root of the right side: 5.04424865 Break this problem into two subproblems by setting (x + -2.333333334) equal to 5.04424865 and -5.04424865.Subproblem 1
x + -2.333333334 = 5.04424865 Simplifying x + -2.333333334 = 5.04424865 Reorder the terms: -2.333333334 + x = 5.04424865 Solving -2.333333334 + x = 5.04424865 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 = 5.04424865 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 5.04424865 + 2.333333334 x = 5.04424865 + 2.333333334 Combine like terms: 5.04424865 + 2.333333334 = 7.377581984 x = 7.377581984 Simplifying x = 7.377581984Subproblem 2
x + -2.333333334 = -5.04424865 Simplifying x + -2.333333334 = -5.04424865 Reorder the terms: -2.333333334 + x = -5.04424865 Solving -2.333333334 + x = -5.04424865 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 = -5.04424865 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -5.04424865 + 2.333333334 x = -5.04424865 + 2.333333334 Combine like terms: -5.04424865 + 2.333333334 = -2.710915316 x = -2.710915316 Simplifying x = -2.710915316Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.377581984, -2.710915316}Solution
x = {7.377581984, -2.710915316}
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