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Simplifying 10x2 + -60x + 52 = 0 Reorder the terms: 52 + -60x + 10x2 = 0 Solving 52 + -60x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(26 + -30x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(26 + -30x + 5x2)' equal to zero and attempt to solve: Simplifying 26 + -30x + 5x2 = 0 Solving 26 + -30x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5.2 + -6x + x2 = 0 Move the constant term to the right: Add '-5.2' to each side of the equation. 5.2 + -6x + -5.2 + x2 = 0 + -5.2 Reorder the terms: 5.2 + -5.2 + -6x + x2 = 0 + -5.2 Combine like terms: 5.2 + -5.2 = 0.0 0.0 + -6x + x2 = 0 + -5.2 -6x + x2 = 0 + -5.2 Combine like terms: 0 + -5.2 = -5.2 -6x + x2 = -5.2 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -5.2 + 9 Reorder the terms: 9 + -6x + x2 = -5.2 + 9 Combine like terms: -5.2 + 9 = 3.8 9 + -6x + x2 = 3.8 Factor a perfect square on the left side: (x + -3)(x + -3) = 3.8 Calculate the square root of the right side: 1.949358869 Break this problem into two subproblems by setting (x + -3) equal to 1.949358869 and -1.949358869.Subproblem 1
x + -3 = 1.949358869 Simplifying x + -3 = 1.949358869 Reorder the terms: -3 + x = 1.949358869 Solving -3 + x = 1.949358869 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1.949358869 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.949358869 + 3 x = 1.949358869 + 3 Combine like terms: 1.949358869 + 3 = 4.949358869 x = 4.949358869 Simplifying x = 4.949358869Subproblem 2
x + -3 = -1.949358869 Simplifying x + -3 = -1.949358869 Reorder the terms: -3 + x = -1.949358869 Solving -3 + x = -1.949358869 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1.949358869 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.949358869 + 3 x = -1.949358869 + 3 Combine like terms: -1.949358869 + 3 = 1.050641131 x = 1.050641131 Simplifying x = 1.050641131Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.949358869, 1.050641131}Solution
x = {4.949358869, 1.050641131}
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