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Simplifying 0 = -0.01x2 + 0.29x + 7.3 Reorder the terms: 0 = 7.3 + 0.29x + -0.01x2 Solving 0 = 7.3 + 0.29x + -0.01x2 Solving for variable 'x'. Combine like terms: 0 + -7.3 = -7.3 -7.3 + -0.29x + 0.01x2 = 7.3 + 0.29x + -0.01x2 + -7.3 + -0.29x + 0.01x2 Reorder the terms: -7.3 + -0.29x + 0.01x2 = 7.3 + -7.3 + 0.29x + -0.29x + -0.01x2 + 0.01x2 Combine like terms: 7.3 + -7.3 = 0.0 -7.3 + -0.29x + 0.01x2 = 0.0 + 0.29x + -0.29x + -0.01x2 + 0.01x2 -7.3 + -0.29x + 0.01x2 = 0.29x + -0.29x + -0.01x2 + 0.01x2 Combine like terms: 0.29x + -0.29x = 0.00 -7.3 + -0.29x + 0.01x2 = 0.00 + -0.01x2 + 0.01x2 -7.3 + -0.29x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 -7.3 + -0.29x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. -730 + -29x + x2 = 0 Move the constant term to the right: Add '730' to each side of the equation. -730 + -29x + 730 + x2 = 0 + 730 Reorder the terms: -730 + 730 + -29x + x2 = 0 + 730 Combine like terms: -730 + 730 = 0 0 + -29x + x2 = 0 + 730 -29x + x2 = 0 + 730 Combine like terms: 0 + 730 = 730 -29x + x2 = 730 The x term is -29x. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x + 210.25 + x2 = 730 + 210.25 Reorder the terms: 210.25 + -29x + x2 = 730 + 210.25 Combine like terms: 730 + 210.25 = 940.25 210.25 + -29x + x2 = 940.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 940.25 Calculate the square root of the right side: 30.663496213 Break this problem into two subproblems by setting (x + -14.5) equal to 30.663496213 and -30.663496213.Subproblem 1
x + -14.5 = 30.663496213 Simplifying x + -14.5 = 30.663496213 Reorder the terms: -14.5 + x = 30.663496213 Solving -14.5 + x = 30.663496213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 30.663496213 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 30.663496213 + 14.5 x = 30.663496213 + 14.5 Combine like terms: 30.663496213 + 14.5 = 45.163496213 x = 45.163496213 Simplifying x = 45.163496213Subproblem 2
x + -14.5 = -30.663496213 Simplifying x + -14.5 = -30.663496213 Reorder the terms: -14.5 + x = -30.663496213 Solving -14.5 + x = -30.663496213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -30.663496213 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -30.663496213 + 14.5 x = -30.663496213 + 14.5 Combine like terms: -30.663496213 + 14.5 = -16.163496213 x = -16.163496213 Simplifying x = -16.163496213Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.163496213, -16.163496213}
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