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Simplifying 14x2 + -66x + -16 = 0 Reorder the terms: -16 + -66x + 14x2 = 0 Solving -16 + -66x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -33x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -33x + 7x2)' equal to zero and attempt to solve: Simplifying -8 + -33x + 7x2 = 0 Solving -8 + -33x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + -4.714285714x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -4.714285714x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -4.714285714x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -4.714285714x + x2 = 0 + 1.142857143 -4.714285714x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -4.714285714x + x2 = 1.142857143 The x term is -4.714285714x. Take half its coefficient (-2.357142857). Square it (5.556122448) and add it to both sides. Add '5.556122448' to each side of the equation. -4.714285714x + 5.556122448 + x2 = 1.142857143 + 5.556122448 Reorder the terms: 5.556122448 + -4.714285714x + x2 = 1.142857143 + 5.556122448 Combine like terms: 1.142857143 + 5.556122448 = 6.698979591 5.556122448 + -4.714285714x + x2 = 6.698979591 Factor a perfect square on the left side: (x + -2.357142857)(x + -2.357142857) = 6.698979591 Calculate the square root of the right side: 2.588238704 Break this problem into two subproblems by setting (x + -2.357142857) equal to 2.588238704 and -2.588238704.Subproblem 1
x + -2.357142857 = 2.588238704 Simplifying x + -2.357142857 = 2.588238704 Reorder the terms: -2.357142857 + x = 2.588238704 Solving -2.357142857 + x = 2.588238704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.357142857' to each side of the equation. -2.357142857 + 2.357142857 + x = 2.588238704 + 2.357142857 Combine like terms: -2.357142857 + 2.357142857 = 0.000000000 0.000000000 + x = 2.588238704 + 2.357142857 x = 2.588238704 + 2.357142857 Combine like terms: 2.588238704 + 2.357142857 = 4.945381561 x = 4.945381561 Simplifying x = 4.945381561Subproblem 2
x + -2.357142857 = -2.588238704 Simplifying x + -2.357142857 = -2.588238704 Reorder the terms: -2.357142857 + x = -2.588238704 Solving -2.357142857 + x = -2.588238704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.357142857' to each side of the equation. -2.357142857 + 2.357142857 + x = -2.588238704 + 2.357142857 Combine like terms: -2.357142857 + 2.357142857 = 0.000000000 0.000000000 + x = -2.588238704 + 2.357142857 x = -2.588238704 + 2.357142857 Combine like terms: -2.588238704 + 2.357142857 = -0.231095847 x = -0.231095847 Simplifying x = -0.231095847Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.945381561, -0.231095847}Solution
x = {4.945381561, -0.231095847}
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