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Simplifying 15x2 + 60x = 55 Reorder the terms: 60x + 15x2 = 55 Solving 60x + 15x2 = 55 Solving for variable 'x'. Reorder the terms: -55 + 60x + 15x2 = 55 + -55 Combine like terms: 55 + -55 = 0 -55 + 60x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-11 + 12x + 3x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-11 + 12x + 3x2)' equal to zero and attempt to solve: Simplifying -11 + 12x + 3x2 = 0 Solving -11 + 12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.666666667 + 4x + x2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + 4x + 3.666666667 + x2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + 4x + x2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + 4x + x2 = 0 + 3.666666667 4x + x2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 4x + x2 = 3.666666667 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 3.666666667 + 4 Reorder the terms: 4 + 4x + x2 = 3.666666667 + 4 Combine like terms: 3.666666667 + 4 = 7.666666667 4 + 4x + x2 = 7.666666667 Factor a perfect square on the left side: (x + 2)(x + 2) = 7.666666667 Calculate the square root of the right side: 2.768874621 Break this problem into two subproblems by setting (x + 2) equal to 2.768874621 and -2.768874621.Subproblem 1
x + 2 = 2.768874621 Simplifying x + 2 = 2.768874621 Reorder the terms: 2 + x = 2.768874621 Solving 2 + x = 2.768874621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.768874621 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.768874621 + -2 x = 2.768874621 + -2 Combine like terms: 2.768874621 + -2 = 0.768874621 x = 0.768874621 Simplifying x = 0.768874621Subproblem 2
x + 2 = -2.768874621 Simplifying x + 2 = -2.768874621 Reorder the terms: 2 + x = -2.768874621 Solving 2 + x = -2.768874621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.768874621 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.768874621 + -2 x = -2.768874621 + -2 Combine like terms: -2.768874621 + -2 = -4.768874621 x = -4.768874621 Simplifying x = -4.768874621Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.768874621, -4.768874621}Solution
x = {0.768874621, -4.768874621}
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