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Simplifying 300 = 0.053x2 + 0.543x + 9.44 Reorder the terms: 300 = 9.44 + 0.543x + 0.053x2 Solving 300 = 9.44 + 0.543x + 0.053x2 Solving for variable 'x'. Combine like terms: 300 + -9.44 = 290.56 290.56 + -0.543x + -0.053x2 = 9.44 + 0.543x + 0.053x2 + -9.44 + -0.543x + -0.053x2 Reorder the terms: 290.56 + -0.543x + -0.053x2 = 9.44 + -9.44 + 0.543x + -0.543x + 0.053x2 + -0.053x2 Combine like terms: 9.44 + -9.44 = 0.00 290.56 + -0.543x + -0.053x2 = 0.00 + 0.543x + -0.543x + 0.053x2 + -0.053x2 290.56 + -0.543x + -0.053x2 = 0.543x + -0.543x + 0.053x2 + -0.053x2 Combine like terms: 0.543x + -0.543x = 0.000 290.56 + -0.543x + -0.053x2 = 0.000 + 0.053x2 + -0.053x2 290.56 + -0.543x + -0.053x2 = 0.053x2 + -0.053x2 Combine like terms: 0.053x2 + -0.053x2 = 0.000 290.56 + -0.543x + -0.053x2 = 0.000 Begin completing the square. Divide all terms by -0.053 the coefficient of the squared term: Divide each side by '-0.053'. -5482.264151 + 10.24528302x + x2 = 0 Move the constant term to the right: Add '5482.264151' to each side of the equation. -5482.264151 + 10.24528302x + 5482.264151 + x2 = 0 + 5482.264151 Reorder the terms: -5482.264151 + 5482.264151 + 10.24528302x + x2 = 0 + 5482.264151 Combine like terms: -5482.264151 + 5482.264151 = 0.000000 0.000000 + 10.24528302x + x2 = 0 + 5482.264151 10.24528302x + x2 = 0 + 5482.264151 Combine like terms: 0 + 5482.264151 = 5482.264151 10.24528302x + x2 = 5482.264151 The x term is 10.24528302x. Take half its coefficient (5.12264151). Square it (26.24145604) and add it to both sides. Add '26.24145604' to each side of the equation. 10.24528302x + 26.24145604 + x2 = 5482.264151 + 26.24145604 Reorder the terms: 26.24145604 + 10.24528302x + x2 = 5482.264151 + 26.24145604 Combine like terms: 5482.264151 + 26.24145604 = 5508.50560704 26.24145604 + 10.24528302x + x2 = 5508.50560704 Factor a perfect square on the left side: (x + 5.12264151)(x + 5.12264151) = 5508.50560704 Calculate the square root of the right side: 74.219307508 Break this problem into two subproblems by setting (x + 5.12264151) equal to 74.219307508 and -74.219307508.Subproblem 1
x + 5.12264151 = 74.219307508 Simplifying x + 5.12264151 = 74.219307508 Reorder the terms: 5.12264151 + x = 74.219307508 Solving 5.12264151 + x = 74.219307508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.12264151' to each side of the equation. 5.12264151 + -5.12264151 + x = 74.219307508 + -5.12264151 Combine like terms: 5.12264151 + -5.12264151 = 0.00000000 0.00000000 + x = 74.219307508 + -5.12264151 x = 74.219307508 + -5.12264151 Combine like terms: 74.219307508 + -5.12264151 = 69.096665998 x = 69.096665998 Simplifying x = 69.096665998Subproblem 2
x + 5.12264151 = -74.219307508 Simplifying x + 5.12264151 = -74.219307508 Reorder the terms: 5.12264151 + x = -74.219307508 Solving 5.12264151 + x = -74.219307508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.12264151' to each side of the equation. 5.12264151 + -5.12264151 + x = -74.219307508 + -5.12264151 Combine like terms: 5.12264151 + -5.12264151 = 0.00000000 0.00000000 + x = -74.219307508 + -5.12264151 x = -74.219307508 + -5.12264151 Combine like terms: -74.219307508 + -5.12264151 = -79.341949018 x = -79.341949018 Simplifying x = -79.341949018Solution
The solution to the problem is based on the solutions from the subproblems. x = {69.096665998, -79.341949018}
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