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Simplifying 0.5x + 0.5x(16 + -1x) = 0.10(-73) 0.5x + (16 * 0.5x + -1x * 0.5x) = 0.10(-73) 0.5x + (8x + -0.5x2) = 0.10(-73) Combine like terms: 0.5x + 8x = 8.5x 8.5x + -0.5x2 = 0.10(-73) Multiply 0.10 * -73 8.5x + -0.5x2 = -7.3 Solving 8.5x + -0.5x2 = -7.3 Solving for variable 'x'. Reorder the terms: 7.3 + 8.5x + -0.5x2 = -7.3 + 7.3 Combine like terms: -7.3 + 7.3 = 0.0 7.3 + 8.5x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -14.6 + -17x + x2 = 0 Move the constant term to the right: Add '14.6' to each side of the equation. -14.6 + -17x + 14.6 + x2 = 0 + 14.6 Reorder the terms: -14.6 + 14.6 + -17x + x2 = 0 + 14.6 Combine like terms: -14.6 + 14.6 = 0.0 0.0 + -17x + x2 = 0 + 14.6 -17x + x2 = 0 + 14.6 Combine like terms: 0 + 14.6 = 14.6 -17x + x2 = 14.6 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = 14.6 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 14.6 + 72.25 Combine like terms: 14.6 + 72.25 = 86.85 72.25 + -17x + x2 = 86.85 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 86.85 Calculate the square root of the right side: 9.31933474 Break this problem into two subproblems by setting (x + -8.5) equal to 9.31933474 and -9.31933474.Subproblem 1
x + -8.5 = 9.31933474 Simplifying x + -8.5 = 9.31933474 Reorder the terms: -8.5 + x = 9.31933474 Solving -8.5 + x = 9.31933474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 9.31933474 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 9.31933474 + 8.5 x = 9.31933474 + 8.5 Combine like terms: 9.31933474 + 8.5 = 17.81933474 x = 17.81933474 Simplifying x = 17.81933474Subproblem 2
x + -8.5 = -9.31933474 Simplifying x + -8.5 = -9.31933474 Reorder the terms: -8.5 + x = -9.31933474 Solving -8.5 + x = -9.31933474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -9.31933474 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -9.31933474 + 8.5 x = -9.31933474 + 8.5 Combine like terms: -9.31933474 + 8.5 = -0.81933474 x = -0.81933474 Simplifying x = -0.81933474Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.81933474, -0.81933474}
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