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Simplifying 14x2 + -60x + 38 = 0 Reorder the terms: 38 + -60x + 14x2 = 0 Solving 38 + -60x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(19 + -30x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19 + -30x + 7x2)' equal to zero and attempt to solve: Simplifying 19 + -30x + 7x2 = 0 Solving 19 + -30x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2.714285714 + -4.285714286x + x2 = 0 Move the constant term to the right: Add '-2.714285714' to each side of the equation. 2.714285714 + -4.285714286x + -2.714285714 + x2 = 0 + -2.714285714 Reorder the terms: 2.714285714 + -2.714285714 + -4.285714286x + x2 = 0 + -2.714285714 Combine like terms: 2.714285714 + -2.714285714 = 0.000000000 0.000000000 + -4.285714286x + x2 = 0 + -2.714285714 -4.285714286x + x2 = 0 + -2.714285714 Combine like terms: 0 + -2.714285714 = -2.714285714 -4.285714286x + x2 = -2.714285714 The x term is -4.285714286x. Take half its coefficient (-2.142857143). Square it (4.591836735) and add it to both sides. Add '4.591836735' to each side of the equation. -4.285714286x + 4.591836735 + x2 = -2.714285714 + 4.591836735 Reorder the terms: 4.591836735 + -4.285714286x + x2 = -2.714285714 + 4.591836735 Combine like terms: -2.714285714 + 4.591836735 = 1.877551021 4.591836735 + -4.285714286x + x2 = 1.877551021 Factor a perfect square on the left side: (x + -2.142857143)(x + -2.142857143) = 1.877551021 Calculate the square root of the right side: 1.370237578 Break this problem into two subproblems by setting (x + -2.142857143) equal to 1.370237578 and -1.370237578.Subproblem 1
x + -2.142857143 = 1.370237578 Simplifying x + -2.142857143 = 1.370237578 Reorder the terms: -2.142857143 + x = 1.370237578 Solving -2.142857143 + x = 1.370237578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.142857143' to each side of the equation. -2.142857143 + 2.142857143 + x = 1.370237578 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + x = 1.370237578 + 2.142857143 x = 1.370237578 + 2.142857143 Combine like terms: 1.370237578 + 2.142857143 = 3.513094721 x = 3.513094721 Simplifying x = 3.513094721Subproblem 2
x + -2.142857143 = -1.370237578 Simplifying x + -2.142857143 = -1.370237578 Reorder the terms: -2.142857143 + x = -1.370237578 Solving -2.142857143 + x = -1.370237578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.142857143' to each side of the equation. -2.142857143 + 2.142857143 + x = -1.370237578 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + x = -1.370237578 + 2.142857143 x = -1.370237578 + 2.142857143 Combine like terms: -1.370237578 + 2.142857143 = 0.772619565 x = 0.772619565 Simplifying x = 0.772619565Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.513094721, 0.772619565}Solution
x = {3.513094721, 0.772619565}
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