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Simplifying 60x + 2 = 14x2 + 14 Reorder the terms: 2 + 60x = 14x2 + 14 Reorder the terms: 2 + 60x = 14 + 14x2 Solving 2 + 60x = 14 + 14x2 Solving for variable 'x'. Reorder the terms: 2 + -14 + 60x + -14x2 = 14 + 14x2 + -14 + -14x2 Combine like terms: 2 + -14 = -12 -12 + 60x + -14x2 = 14 + 14x2 + -14 + -14x2 Reorder the terms: -12 + 60x + -14x2 = 14 + -14 + 14x2 + -14x2 Combine like terms: 14 + -14 = 0 -12 + 60x + -14x2 = 0 + 14x2 + -14x2 -12 + 60x + -14x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 -12 + 60x + -14x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 30x + -7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 30x + -7x2)' equal to zero and attempt to solve: Simplifying -6 + 30x + -7x2 = 0 Solving -6 + 30x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 0.8571428571 + -4.285714286x + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + -4.285714286x + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + -4.285714286x + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + -4.285714286x + x2 = 0 + -0.8571428571 -4.285714286x + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 -4.285714286x + x2 = -0.8571428571 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 = -0.8571428571 + 4.591836735 Reorder the terms: 4.591836735 + -4.285714286x + x2 = -0.8571428571 + 4.591836735 Combine like terms: -0.8571428571 + 4.591836735 = 3.7346938779 4.591836735 + -4.285714286x + x2 = 3.7346938779 Factor a perfect square on the left side: (x + -2.142857143)(x + -2.142857143) = 3.7346938779 Calculate the square root of the right side: 1.932535608 Break this problem into two subproblems by setting (x + -2.142857143) equal to 1.932535608 and -1.932535608.Subproblem 1
x + -2.142857143 = 1.932535608 Simplifying x + -2.142857143 = 1.932535608 Reorder the terms: -2.142857143 + x = 1.932535608 Solving -2.142857143 + x = 1.932535608 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 = 1.932535608 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + x = 1.932535608 + 2.142857143 x = 1.932535608 + 2.142857143 Combine like terms: 1.932535608 + 2.142857143 = 4.075392751 x = 4.075392751 Simplifying x = 4.075392751Subproblem 2
x + -2.142857143 = -1.932535608 Simplifying x + -2.142857143 = -1.932535608 Reorder the terms: -2.142857143 + x = -1.932535608 Solving -2.142857143 + x = -1.932535608 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 = -1.932535608 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + x = -1.932535608 + 2.142857143 x = -1.932535608 + 2.142857143 Combine like terms: -1.932535608 + 2.142857143 = 0.210321535 x = 0.210321535 Simplifying x = 0.210321535Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.075392751, 0.210321535}Solution
x = {4.075392751, 0.210321535}
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