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Simplifying 2x2 + -15x = 47 Reorder the terms: -15x + 2x2 = 47 Solving -15x + 2x2 = 47 Solving for variable 'x'. Reorder the terms: -47 + -15x + 2x2 = 47 + -47 Combine like terms: 47 + -47 = 0 -47 + -15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -23.5 + -7.5x + x2 = 0 Move the constant term to the right: Add '23.5' to each side of the equation. -23.5 + -7.5x + 23.5 + x2 = 0 + 23.5 Reorder the terms: -23.5 + 23.5 + -7.5x + x2 = 0 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + -7.5x + x2 = 0 + 23.5 -7.5x + x2 = 0 + 23.5 Combine like terms: 0 + 23.5 = 23.5 -7.5x + x2 = 23.5 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 23.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 23.5 + 14.0625 Combine like terms: 23.5 + 14.0625 = 37.5625 14.0625 + -7.5x + x2 = 37.5625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 37.5625 Calculate the square root of the right side: 6.128825336 Break this problem into two subproblems by setting (x + -3.75) equal to 6.128825336 and -6.128825336.Subproblem 1
x + -3.75 = 6.128825336 Simplifying x + -3.75 = 6.128825336 Reorder the terms: -3.75 + x = 6.128825336 Solving -3.75 + x = 6.128825336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 6.128825336 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 6.128825336 + 3.75 x = 6.128825336 + 3.75 Combine like terms: 6.128825336 + 3.75 = 9.878825336 x = 9.878825336 Simplifying x = 9.878825336Subproblem 2
x + -3.75 = -6.128825336 Simplifying x + -3.75 = -6.128825336 Reorder the terms: -3.75 + x = -6.128825336 Solving -3.75 + x = -6.128825336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -6.128825336 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -6.128825336 + 3.75 x = -6.128825336 + 3.75 Combine like terms: -6.128825336 + 3.75 = -2.378825336 x = -2.378825336 Simplifying x = -2.378825336Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.878825336, -2.378825336}
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