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Simplifying 44 = 15x + (0.5)(5)(x2) Multiply 0.5 * 5 44 = 15x + 2.5x2 Solving 44 = 15x + 2.5x2 Solving for variable 'x'. Reorder the terms: 44 + -15x + -2.5x2 = 15x + -15x + 2.5x2 + -2.5x2 Combine like terms: 15x + -15x = 0 44 + -15x + -2.5x2 = 0 + 2.5x2 + -2.5x2 44 + -15x + -2.5x2 = 2.5x2 + -2.5x2 Combine like terms: 2.5x2 + -2.5x2 = 0.0 44 + -15x + -2.5x2 = 0.0 Begin completing the square. Divide all terms by -2.5 the coefficient of the squared term: Divide each side by '-2.5'. -17.6 + 6x + x2 = 0 Move the constant term to the right: Add '17.6' to each side of the equation. -17.6 + 6x + 17.6 + x2 = 0 + 17.6 Reorder the terms: -17.6 + 17.6 + 6x + x2 = 0 + 17.6 Combine like terms: -17.6 + 17.6 = 0.0 0.0 + 6x + x2 = 0 + 17.6 6x + x2 = 0 + 17.6 Combine like terms: 0 + 17.6 = 17.6 6x + x2 = 17.6 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 17.6 + 9 Reorder the terms: 9 + 6x + x2 = 17.6 + 9 Combine like terms: 17.6 + 9 = 26.6 9 + 6x + x2 = 26.6 Factor a perfect square on the left side: (x + 3)(x + 3) = 26.6 Calculate the square root of the right side: 5.157518783 Break this problem into two subproblems by setting (x + 3) equal to 5.157518783 and -5.157518783.Subproblem 1
x + 3 = 5.157518783 Simplifying x + 3 = 5.157518783 Reorder the terms: 3 + x = 5.157518783 Solving 3 + x = 5.157518783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.157518783 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.157518783 + -3 x = 5.157518783 + -3 Combine like terms: 5.157518783 + -3 = 2.157518783 x = 2.157518783 Simplifying x = 2.157518783Subproblem 2
x + 3 = -5.157518783 Simplifying x + 3 = -5.157518783 Reorder the terms: 3 + x = -5.157518783 Solving 3 + x = -5.157518783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.157518783 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.157518783 + -3 x = -5.157518783 + -3 Combine like terms: -5.157518783 + -3 = -8.157518783 x = -8.157518783 Simplifying x = -8.157518783Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.157518783, -8.157518783}
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