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Simplifying 15x2 = 408(x + 2) Reorder the terms: 15x2 = 408(2 + x) 15x2 = (2 * 408 + x * 408) 15x2 = (816 + 408x) Solving 15x2 = 816 + 408x Solving for variable 'x'. Reorder the terms: -816 + -408x + 15x2 = 816 + 408x + -816 + -408x Reorder the terms: -816 + -408x + 15x2 = 816 + -816 + 408x + -408x Combine like terms: 816 + -816 = 0 -816 + -408x + 15x2 = 0 + 408x + -408x -816 + -408x + 15x2 = 408x + -408x Combine like terms: 408x + -408x = 0 -816 + -408x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-272 + -136x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-272 + -136x + 5x2)' equal to zero and attempt to solve: Simplifying -272 + -136x + 5x2 = 0 Solving -272 + -136x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -54.4 + -27.2x + x2 = 0 Move the constant term to the right: Add '54.4' to each side of the equation. -54.4 + -27.2x + 54.4 + x2 = 0 + 54.4 Reorder the terms: -54.4 + 54.4 + -27.2x + x2 = 0 + 54.4 Combine like terms: -54.4 + 54.4 = 0.0 0.0 + -27.2x + x2 = 0 + 54.4 -27.2x + x2 = 0 + 54.4 Combine like terms: 0 + 54.4 = 54.4 -27.2x + x2 = 54.4 The x term is -27.2x. Take half its coefficient (-13.6). Square it (184.96) and add it to both sides. Add '184.96' to each side of the equation. -27.2x + 184.96 + x2 = 54.4 + 184.96 Reorder the terms: 184.96 + -27.2x + x2 = 54.4 + 184.96 Combine like terms: 54.4 + 184.96 = 239.36 184.96 + -27.2x + x2 = 239.36 Factor a perfect square on the left side: (x + -13.6)(x + -13.6) = 239.36 Calculate the square root of the right side: 15.471263685 Break this problem into two subproblems by setting (x + -13.6) equal to 15.471263685 and -15.471263685.Subproblem 1
x + -13.6 = 15.471263685 Simplifying x + -13.6 = 15.471263685 Reorder the terms: -13.6 + x = 15.471263685 Solving -13.6 + x = 15.471263685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.6' to each side of the equation. -13.6 + 13.6 + x = 15.471263685 + 13.6 Combine like terms: -13.6 + 13.6 = 0.0 0.0 + x = 15.471263685 + 13.6 x = 15.471263685 + 13.6 Combine like terms: 15.471263685 + 13.6 = 29.071263685 x = 29.071263685 Simplifying x = 29.071263685Subproblem 2
x + -13.6 = -15.471263685 Simplifying x + -13.6 = -15.471263685 Reorder the terms: -13.6 + x = -15.471263685 Solving -13.6 + x = -15.471263685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.6' to each side of the equation. -13.6 + 13.6 + x = -15.471263685 + 13.6 Combine like terms: -13.6 + 13.6 = 0.0 0.0 + x = -15.471263685 + 13.6 x = -15.471263685 + 13.6 Combine like terms: -15.471263685 + 13.6 = -1.871263685 x = -1.871263685 Simplifying x = -1.871263685Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.071263685, -1.871263685}Solution
x = {29.071263685, -1.871263685}
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