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Simplifying 10x2 + 64x + 60 = 0 Reorder the terms: 60 + 64x + 10x2 = 0 Solving 60 + 64x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(30 + 32x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(30 + 32x + 5x2)' equal to zero and attempt to solve: Simplifying 30 + 32x + 5x2 = 0 Solving 30 + 32x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 6 + 6.4x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 6.4x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 6.4x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 6.4x + x2 = 0 + -6 6.4x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 6.4x + x2 = -6 The x term is 6.4x. Take half its coefficient (3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. 6.4x + 10.24 + x2 = -6 + 10.24 Reorder the terms: 10.24 + 6.4x + x2 = -6 + 10.24 Combine like terms: -6 + 10.24 = 4.24 10.24 + 6.4x + x2 = 4.24 Factor a perfect square on the left side: (x + 3.2)(x + 3.2) = 4.24 Calculate the square root of the right side: 2.059126028 Break this problem into two subproblems by setting (x + 3.2) equal to 2.059126028 and -2.059126028.Subproblem 1
x + 3.2 = 2.059126028 Simplifying x + 3.2 = 2.059126028 Reorder the terms: 3.2 + x = 2.059126028 Solving 3.2 + x = 2.059126028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = 2.059126028 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = 2.059126028 + -3.2 x = 2.059126028 + -3.2 Combine like terms: 2.059126028 + -3.2 = -1.140873972 x = -1.140873972 Simplifying x = -1.140873972Subproblem 2
x + 3.2 = -2.059126028 Simplifying x + 3.2 = -2.059126028 Reorder the terms: 3.2 + x = -2.059126028 Solving 3.2 + x = -2.059126028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = -2.059126028 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = -2.059126028 + -3.2 x = -2.059126028 + -3.2 Combine like terms: -2.059126028 + -3.2 = -5.259126028 x = -5.259126028 Simplifying x = -5.259126028Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.140873972, -5.259126028}Solution
x = {-1.140873972, -5.259126028}
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