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Simplifying 10x2 + -66x + 72 = 0 Reorder the terms: 72 + -66x + 10x2 = 0 Solving 72 + -66x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(36 + -33x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(36 + -33x + 5x2)' equal to zero and attempt to solve: Simplifying 36 + -33x + 5x2 = 0 Solving 36 + -33x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 7.2 + -6.6x + x2 = 0 Move the constant term to the right: Add '-7.2' to each side of the equation. 7.2 + -6.6x + -7.2 + x2 = 0 + -7.2 Reorder the terms: 7.2 + -7.2 + -6.6x + x2 = 0 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + -6.6x + x2 = 0 + -7.2 -6.6x + x2 = 0 + -7.2 Combine like terms: 0 + -7.2 = -7.2 -6.6x + x2 = -7.2 The x term is -6.6x. Take half its coefficient (-3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. -6.6x + 10.89 + x2 = -7.2 + 10.89 Reorder the terms: 10.89 + -6.6x + x2 = -7.2 + 10.89 Combine like terms: -7.2 + 10.89 = 3.69 10.89 + -6.6x + x2 = 3.69 Factor a perfect square on the left side: (x + -3.3)(x + -3.3) = 3.69 Calculate the square root of the right side: 1.920937271 Break this problem into two subproblems by setting (x + -3.3) equal to 1.920937271 and -1.920937271.Subproblem 1
x + -3.3 = 1.920937271 Simplifying x + -3.3 = 1.920937271 Reorder the terms: -3.3 + x = 1.920937271 Solving -3.3 + x = 1.920937271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + x = 1.920937271 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = 1.920937271 + 3.3 x = 1.920937271 + 3.3 Combine like terms: 1.920937271 + 3.3 = 5.220937271 x = 5.220937271 Simplifying x = 5.220937271Subproblem 2
x + -3.3 = -1.920937271 Simplifying x + -3.3 = -1.920937271 Reorder the terms: -3.3 + x = -1.920937271 Solving -3.3 + x = -1.920937271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + x = -1.920937271 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = -1.920937271 + 3.3 x = -1.920937271 + 3.3 Combine like terms: -1.920937271 + 3.3 = 1.379062729 x = 1.379062729 Simplifying x = 1.379062729Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.220937271, 1.379062729}Solution
x = {5.220937271, 1.379062729}
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