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Simplifying 0 = 12x2 + -60x + 50 Reorder the terms: 0 = 50 + -60x + 12x2 Solving 0 = 50 + -60x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -50 = -50 -50 + 60x + -12x2 = 50 + -60x + 12x2 + -50 + 60x + -12x2 Reorder the terms: -50 + 60x + -12x2 = 50 + -50 + -60x + 60x + 12x2 + -12x2 Combine like terms: 50 + -50 = 0 -50 + 60x + -12x2 = 0 + -60x + 60x + 12x2 + -12x2 -50 + 60x + -12x2 = -60x + 60x + 12x2 + -12x2 Combine like terms: -60x + 60x = 0 -50 + 60x + -12x2 = 0 + 12x2 + -12x2 -50 + 60x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -50 + 60x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + 30x + -6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + 30x + -6x2)' equal to zero and attempt to solve: Simplifying -25 + 30x + -6x2 = 0 Solving -25 + 30x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 4.166666667 + -5x + x2 = 0 Move the constant term to the right: Add '-4.166666667' to each side of the equation. 4.166666667 + -5x + -4.166666667 + x2 = 0 + -4.166666667 Reorder the terms: 4.166666667 + -4.166666667 + -5x + x2 = 0 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + -5x + x2 = 0 + -4.166666667 -5x + x2 = 0 + -4.166666667 Combine like terms: 0 + -4.166666667 = -4.166666667 -5x + x2 = -4.166666667 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -4.166666667 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -4.166666667 + 6.25 Combine like terms: -4.166666667 + 6.25 = 2.083333333 6.25 + -5x + x2 = 2.083333333 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 2.083333333 Calculate the square root of the right side: 1.443375673 Break this problem into two subproblems by setting (x + -2.5) equal to 1.443375673 and -1.443375673.Subproblem 1
x + -2.5 = 1.443375673 Simplifying x + -2.5 = 1.443375673 Reorder the terms: -2.5 + x = 1.443375673 Solving -2.5 + x = 1.443375673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.443375673 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.443375673 + 2.5 x = 1.443375673 + 2.5 Combine like terms: 1.443375673 + 2.5 = 3.943375673 x = 3.943375673 Simplifying x = 3.943375673Subproblem 2
x + -2.5 = -1.443375673 Simplifying x + -2.5 = -1.443375673 Reorder the terms: -2.5 + x = -1.443375673 Solving -2.5 + x = -1.443375673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.443375673 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.443375673 + 2.5 x = -1.443375673 + 2.5 Combine like terms: -1.443375673 + 2.5 = 1.056624327 x = 1.056624327 Simplifying x = 1.056624327Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.943375673, 1.056624327}Solution
x = {3.943375673, 1.056624327}
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