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Simplifying 2(x + -9) + -7x(6 + -4x) = 0 Reorder the terms: 2(-9 + x) + -7x(6 + -4x) = 0 (-9 * 2 + x * 2) + -7x(6 + -4x) = 0 (-18 + 2x) + -7x(6 + -4x) = 0 -18 + 2x + (6 * -7x + -4x * -7x) = 0 -18 + 2x + (-42x + 28x2) = 0 Combine like terms: 2x + -42x = -40x -18 + -40x + 28x2 = 0 Solving -18 + -40x + 28x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -20x + 14x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -20x + 14x2)' equal to zero and attempt to solve: Simplifying -9 + -20x + 14x2 = 0 Solving -9 + -20x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.6428571429 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '0.6428571429' to each side of the equation. -0.6428571429 + -1.428571429x + 0.6428571429 + x2 = 0 + 0.6428571429 Reorder the terms: -0.6428571429 + 0.6428571429 + -1.428571429x + x2 = 0 + 0.6428571429 Combine like terms: -0.6428571429 + 0.6428571429 = 0.0000000000 0.0000000000 + -1.428571429x + x2 = 0 + 0.6428571429 -1.428571429x + x2 = 0 + 0.6428571429 Combine like terms: 0 + 0.6428571429 = 0.6428571429 -1.428571429x + x2 = 0.6428571429 The x term is -1.428571429x. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429x + 0.5102040819 + x2 = 0.6428571429 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = 0.6428571429 + 0.5102040819 Combine like terms: 0.6428571429 + 0.5102040819 = 1.1530612248 0.5102040819 + -1.428571429x + x2 = 1.1530612248 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 1.1530612248 Calculate the square root of the right side: 1.073806884 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 1.073806884 and -1.073806884.Subproblem 1
x + -0.7142857145 = 1.073806884 Simplifying x + -0.7142857145 = 1.073806884 Reorder the terms: -0.7142857145 + x = 1.073806884 Solving -0.7142857145 + x = 1.073806884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = 1.073806884 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 1.073806884 + 0.7142857145 x = 1.073806884 + 0.7142857145 Combine like terms: 1.073806884 + 0.7142857145 = 1.7880925985 x = 1.7880925985 Simplifying x = 1.7880925985Subproblem 2
x + -0.7142857145 = -1.073806884 Simplifying x + -0.7142857145 = -1.073806884 Reorder the terms: -0.7142857145 + x = -1.073806884 Solving -0.7142857145 + x = -1.073806884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = -1.073806884 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -1.073806884 + 0.7142857145 x = -1.073806884 + 0.7142857145 Combine like terms: -1.073806884 + 0.7142857145 = -0.3595211695 x = -0.3595211695 Simplifying x = -0.3595211695Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7880925985, -0.3595211695}Solution
x = {1.7880925985, -0.3595211695}
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