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Simplifying 60x + -12 = 14x2 + 2 Reorder the terms: -12 + 60x = 14x2 + 2 Reorder the terms: -12 + 60x = 2 + 14x2 Solving -12 + 60x = 2 + 14x2 Solving for variable 'x'. Reorder the terms: -12 + -2 + 60x + -14x2 = 2 + 14x2 + -2 + -14x2 Combine like terms: -12 + -2 = -14 -14 + 60x + -14x2 = 2 + 14x2 + -2 + -14x2 Reorder the terms: -14 + 60x + -14x2 = 2 + -2 + 14x2 + -14x2 Combine like terms: 2 + -2 = 0 -14 + 60x + -14x2 = 0 + 14x2 + -14x2 -14 + 60x + -14x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 -14 + 60x + -14x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 30x + -7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 30x + -7x2)' equal to zero and attempt to solve: Simplifying -7 + 30x + -7x2 = 0 Solving -7 + 30x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 1 + -4.285714286x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4.285714286x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -4.285714286x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4.285714286x + x2 = 0 + -1 -4.285714286x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4.285714286x + x2 = -1 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 + 4.591836735 Reorder the terms: 4.591836735 + -4.285714286x + x2 = -1 + 4.591836735 Combine like terms: -1 + 4.591836735 = 3.591836735 4.591836735 + -4.285714286x + x2 = 3.591836735 Factor a perfect square on the left side: (x + -2.142857143)(x + -2.142857143) = 3.591836735 Calculate the square root of the right side: 1.895214166 Break this problem into two subproblems by setting (x + -2.142857143) equal to 1.895214166 and -1.895214166.Subproblem 1
x + -2.142857143 = 1.895214166 Simplifying x + -2.142857143 = 1.895214166 Reorder the terms: -2.142857143 + x = 1.895214166 Solving -2.142857143 + x = 1.895214166 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 = 1.895214166 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + x = 1.895214166 + 2.142857143 x = 1.895214166 + 2.142857143 Combine like terms: 1.895214166 + 2.142857143 = 4.038071309 x = 4.038071309 Simplifying x = 4.038071309Subproblem 2
x + -2.142857143 = -1.895214166 Simplifying x + -2.142857143 = -1.895214166 Reorder the terms: -2.142857143 + x = -1.895214166 Solving -2.142857143 + x = -1.895214166 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 = -1.895214166 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + x = -1.895214166 + 2.142857143 x = -1.895214166 + 2.142857143 Combine like terms: -1.895214166 + 2.142857143 = 0.247642977 x = 0.247642977 Simplifying x = 0.247642977Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.038071309, 0.247642977}Solution
x = {4.038071309, 0.247642977}
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