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Simplifying 27 + 21 + 2x + 4x2 = 115 Combine like terms: 27 + 21 = 48 48 + 2x + 4x2 = 115 Solving 48 + 2x + 4x2 = 115 Solving for variable 'x'. Reorder the terms: 48 + -115 + 2x + 4x2 = 115 + -115 Combine like terms: 48 + -115 = -67 -67 + 2x + 4x2 = 115 + -115 Combine like terms: 115 + -115 = 0 -67 + 2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -16.75 + 0.5x + x2 = 0 Move the constant term to the right: Add '16.75' to each side of the equation. -16.75 + 0.5x + 16.75 + x2 = 0 + 16.75 Reorder the terms: -16.75 + 16.75 + 0.5x + x2 = 0 + 16.75 Combine like terms: -16.75 + 16.75 = 0.00 0.00 + 0.5x + x2 = 0 + 16.75 0.5x + x2 = 0 + 16.75 Combine like terms: 0 + 16.75 = 16.75 0.5x + x2 = 16.75 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 16.75 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 16.75 + 0.0625 Combine like terms: 16.75 + 0.0625 = 16.8125 0.0625 + 0.5x + x2 = 16.8125 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 16.8125 Calculate the square root of the right side: 4.100304867 Break this problem into two subproblems by setting (x + 0.25) equal to 4.100304867 and -4.100304867.Subproblem 1
x + 0.25 = 4.100304867 Simplifying x + 0.25 = 4.100304867 Reorder the terms: 0.25 + x = 4.100304867 Solving 0.25 + x = 4.100304867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 4.100304867 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 4.100304867 + -0.25 x = 4.100304867 + -0.25 Combine like terms: 4.100304867 + -0.25 = 3.850304867 x = 3.850304867 Simplifying x = 3.850304867Subproblem 2
x + 0.25 = -4.100304867 Simplifying x + 0.25 = -4.100304867 Reorder the terms: 0.25 + x = -4.100304867 Solving 0.25 + x = -4.100304867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -4.100304867 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -4.100304867 + -0.25 x = -4.100304867 + -0.25 Combine like terms: -4.100304867 + -0.25 = -4.350304867 x = -4.350304867 Simplifying x = -4.350304867Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.850304867, -4.350304867}
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