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Simplifying 10x2 = 60x + 2 Reorder the terms: 10x2 = 2 + 60x Solving 10x2 = 2 + 60x Solving for variable 'x'. Reorder the terms: -2 + -60x + 10x2 = 2 + 60x + -2 + -60x Reorder the terms: -2 + -60x + 10x2 = 2 + -2 + 60x + -60x Combine like terms: 2 + -2 = 0 -2 + -60x + 10x2 = 0 + 60x + -60x -2 + -60x + 10x2 = 60x + -60x Combine like terms: 60x + -60x = 0 -2 + -60x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -30x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -30x + 5x2)' equal to zero and attempt to solve: Simplifying -1 + -30x + 5x2 = 0 Solving -1 + -30x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -6x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -6x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -6x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -6x + x2 = 0 + 0.2 -6x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -6x + x2 = 0.2 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 = 0.2 + 9 Reorder the terms: 9 + -6x + x2 = 0.2 + 9 Combine like terms: 0.2 + 9 = 9.2 9 + -6x + x2 = 9.2 Factor a perfect square on the left side: (x + -3)(x + -3) = 9.2 Calculate the square root of the right side: 3.033150178 Break this problem into two subproblems by setting (x + -3) equal to 3.033150178 and -3.033150178.Subproblem 1
x + -3 = 3.033150178 Simplifying x + -3 = 3.033150178 Reorder the terms: -3 + x = 3.033150178 Solving -3 + x = 3.033150178 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 = 3.033150178 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.033150178 + 3 x = 3.033150178 + 3 Combine like terms: 3.033150178 + 3 = 6.033150178 x = 6.033150178 Simplifying x = 6.033150178Subproblem 2
x + -3 = -3.033150178 Simplifying x + -3 = -3.033150178 Reorder the terms: -3 + x = -3.033150178 Solving -3 + x = -3.033150178 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 = -3.033150178 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.033150178 + 3 x = -3.033150178 + 3 Combine like terms: -3.033150178 + 3 = -0.033150178 x = -0.033150178 Simplifying x = -0.033150178Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.033150178, -0.033150178}Solution
x = {6.033150178, -0.033150178}
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