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Simplifying 14x2 + -60x + 40 = 0 Reorder the terms: 40 + -60x + 14x2 = 0 Solving 40 + -60x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(20 + -30x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(20 + -30x + 7x2)' equal to zero and attempt to solve: Simplifying 20 + -30x + 7x2 = 0 Solving 20 + -30x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2.857142857 + -4.285714286x + x2 = 0 Move the constant term to the right: Add '-2.857142857' to each side of the equation. 2.857142857 + -4.285714286x + -2.857142857 + x2 = 0 + -2.857142857 Reorder the terms: 2.857142857 + -2.857142857 + -4.285714286x + x2 = 0 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + -4.285714286x + x2 = 0 + -2.857142857 -4.285714286x + x2 = 0 + -2.857142857 Combine like terms: 0 + -2.857142857 = -2.857142857 -4.285714286x + x2 = -2.857142857 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 = -2.857142857 + 4.591836735 Reorder the terms: 4.591836735 + -4.285714286x + x2 = -2.857142857 + 4.591836735 Combine like terms: -2.857142857 + 4.591836735 = 1.734693878 4.591836735 + -4.285714286x + x2 = 1.734693878 Factor a perfect square on the left side: (x + -2.142857143)(x + -2.142857143) = 1.734693878 Calculate the square root of the right side: 1.31707778 Break this problem into two subproblems by setting (x + -2.142857143) equal to 1.31707778 and -1.31707778.Subproblem 1
x + -2.142857143 = 1.31707778 Simplifying x + -2.142857143 = 1.31707778 Reorder the terms: -2.142857143 + x = 1.31707778 Solving -2.142857143 + x = 1.31707778 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 = 1.31707778 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + x = 1.31707778 + 2.142857143 x = 1.31707778 + 2.142857143 Combine like terms: 1.31707778 + 2.142857143 = 3.459934923 x = 3.459934923 Simplifying x = 3.459934923Subproblem 2
x + -2.142857143 = -1.31707778 Simplifying x + -2.142857143 = -1.31707778 Reorder the terms: -2.142857143 + x = -1.31707778 Solving -2.142857143 + x = -1.31707778 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 = -1.31707778 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + x = -1.31707778 + 2.142857143 x = -1.31707778 + 2.142857143 Combine like terms: -1.31707778 + 2.142857143 = 0.825779363 x = 0.825779363 Simplifying x = 0.825779363Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.459934923, 0.825779363}Solution
x = {3.459934923, 0.825779363}
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