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Simplifying 0 = 2x2 + 15x + -5.5 Reorder the terms: 0 = -5.5 + 15x + 2x2 Solving 0 = -5.5 + 15x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 5.5 = 5.5 5.5 + -15x + -2x2 = -5.5 + 15x + 2x2 + 5.5 + -15x + -2x2 Reorder the terms: 5.5 + -15x + -2x2 = -5.5 + 5.5 + 15x + -15x + 2x2 + -2x2 Combine like terms: -5.5 + 5.5 = 0.0 5.5 + -15x + -2x2 = 0.0 + 15x + -15x + 2x2 + -2x2 5.5 + -15x + -2x2 = 15x + -15x + 2x2 + -2x2 Combine like terms: 15x + -15x = 0 5.5 + -15x + -2x2 = 0 + 2x2 + -2x2 5.5 + -15x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 5.5 + -15x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.75 + 7.5x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 7.5x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 7.5x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 7.5x + x2 = 0 + 2.75 7.5x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 7.5x + x2 = 2.75 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 = 2.75 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 2.75 + 14.0625 Combine like terms: 2.75 + 14.0625 = 16.8125 14.0625 + 7.5x + x2 = 16.8125 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 16.8125 Calculate the square root of the right side: 4.100304867 Break this problem into two subproblems by setting (x + 3.75) equal to 4.100304867 and -4.100304867.Subproblem 1
x + 3.75 = 4.100304867 Simplifying x + 3.75 = 4.100304867 Reorder the terms: 3.75 + x = 4.100304867 Solving 3.75 + x = 4.100304867 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 = 4.100304867 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 4.100304867 + -3.75 x = 4.100304867 + -3.75 Combine like terms: 4.100304867 + -3.75 = 0.350304867 x = 0.350304867 Simplifying x = 0.350304867Subproblem 2
x + 3.75 = -4.100304867 Simplifying x + 3.75 = -4.100304867 Reorder the terms: 3.75 + x = -4.100304867 Solving 3.75 + x = -4.100304867 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 = -4.100304867 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -4.100304867 + -3.75 x = -4.100304867 + -3.75 Combine like terms: -4.100304867 + -3.75 = -7.850304867 x = -7.850304867 Simplifying x = -7.850304867Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.350304867, -7.850304867}
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