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Simplifying 4x2 + 36x + -47 = 0 Reorder the terms: -47 + 36x + 4x2 = 0 Solving -47 + 36x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11.75 + 9x + x2 = 0 Move the constant term to the right: Add '11.75' to each side of the equation. -11.75 + 9x + 11.75 + x2 = 0 + 11.75 Reorder the terms: -11.75 + 11.75 + 9x + x2 = 0 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + 9x + x2 = 0 + 11.75 9x + x2 = 0 + 11.75 Combine like terms: 0 + 11.75 = 11.75 9x + x2 = 11.75 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 11.75 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 11.75 + 20.25 Combine like terms: 11.75 + 20.25 = 32 20.25 + 9x + x2 = 32 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + 4.5) equal to 5.656854249 and -5.656854249.Subproblem 1
x + 4.5 = 5.656854249 Simplifying x + 4.5 = 5.656854249 Reorder the terms: 4.5 + x = 5.656854249 Solving 4.5 + x = 5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 5.656854249 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.656854249 + -4.5 x = 5.656854249 + -4.5 Combine like terms: 5.656854249 + -4.5 = 1.156854249 x = 1.156854249 Simplifying x = 1.156854249Subproblem 2
x + 4.5 = -5.656854249 Simplifying x + 4.5 = -5.656854249 Reorder the terms: 4.5 + x = -5.656854249 Solving 4.5 + x = -5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -5.656854249 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.656854249 + -4.5 x = -5.656854249 + -4.5 Combine like terms: -5.656854249 + -4.5 = -10.156854249 x = -10.156854249 Simplifying x = -10.156854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.156854249, -10.156854249}
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