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Simplifying 60x = 14x2 + 26 Reorder the terms: 60x = 26 + 14x2 Solving 60x = 26 + 14x2 Solving for variable 'x'. Reorder the terms: -26 + 60x + -14x2 = 26 + 14x2 + -26 + -14x2 Reorder the terms: -26 + 60x + -14x2 = 26 + -26 + 14x2 + -14x2 Combine like terms: 26 + -26 = 0 -26 + 60x + -14x2 = 0 + 14x2 + -14x2 -26 + 60x + -14x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 -26 + 60x + -14x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + 30x + -7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + 30x + -7x2)' equal to zero and attempt to solve: Simplifying -13 + 30x + -7x2 = 0 Solving -13 + 30x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 1.857142857 + -4.285714286x + x2 = 0 Move the constant term to the right: Add '-1.857142857' to each side of the equation. 1.857142857 + -4.285714286x + -1.857142857 + x2 = 0 + -1.857142857 Reorder the terms: 1.857142857 + -1.857142857 + -4.285714286x + x2 = 0 + -1.857142857 Combine like terms: 1.857142857 + -1.857142857 = 0.000000000 0.000000000 + -4.285714286x + x2 = 0 + -1.857142857 -4.285714286x + x2 = 0 + -1.857142857 Combine like terms: 0 + -1.857142857 = -1.857142857 -4.285714286x + x2 = -1.857142857 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 = -1.857142857 + 4.591836735 Reorder the terms: 4.591836735 + -4.285714286x + x2 = -1.857142857 + 4.591836735 Combine like terms: -1.857142857 + 4.591836735 = 2.734693878 4.591836735 + -4.285714286x + x2 = 2.734693878 Factor a perfect square on the left side: (x + -2.142857143)(x + -2.142857143) = 2.734693878 Calculate the square root of the right side: 1.653690986 Break this problem into two subproblems by setting (x + -2.142857143) equal to 1.653690986 and -1.653690986.Subproblem 1
x + -2.142857143 = 1.653690986 Simplifying x + -2.142857143 = 1.653690986 Reorder the terms: -2.142857143 + x = 1.653690986 Solving -2.142857143 + x = 1.653690986 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 = 1.653690986 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + x = 1.653690986 + 2.142857143 x = 1.653690986 + 2.142857143 Combine like terms: 1.653690986 + 2.142857143 = 3.796548129 x = 3.796548129 Simplifying x = 3.796548129Subproblem 2
x + -2.142857143 = -1.653690986 Simplifying x + -2.142857143 = -1.653690986 Reorder the terms: -2.142857143 + x = -1.653690986 Solving -2.142857143 + x = -1.653690986 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 = -1.653690986 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + x = -1.653690986 + 2.142857143 x = -1.653690986 + 2.142857143 Combine like terms: -1.653690986 + 2.142857143 = 0.489166157 x = 0.489166157 Simplifying x = 0.489166157Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.796548129, 0.489166157}Solution
x = {3.796548129, 0.489166157}
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