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Simplifying 49x2 + -12.5x + -45 = 0 Reorder the terms: -45 + -12.5x + 49x2 = 0 Solving -45 + -12.5x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.9183673469 + -0.2551020408x + x2 = 0 Move the constant term to the right: Add '0.9183673469' to each side of the equation. -0.9183673469 + -0.2551020408x + 0.9183673469 + x2 = 0 + 0.9183673469 Reorder the terms: -0.9183673469 + 0.9183673469 + -0.2551020408x + x2 = 0 + 0.9183673469 Combine like terms: -0.9183673469 + 0.9183673469 = 0.0000000000 0.0000000000 + -0.2551020408x + x2 = 0 + 0.9183673469 -0.2551020408x + x2 = 0 + 0.9183673469 Combine like terms: 0 + 0.9183673469 = 0.9183673469 -0.2551020408x + x2 = 0.9183673469 The x term is -0.2551020408x. Take half its coefficient (-0.1275510204). Square it (0.01626926281) and add it to both sides. Add '0.01626926281' to each side of the equation. -0.2551020408x + 0.01626926281 + x2 = 0.9183673469 + 0.01626926281 Reorder the terms: 0.01626926281 + -0.2551020408x + x2 = 0.9183673469 + 0.01626926281 Combine like terms: 0.9183673469 + 0.01626926281 = 0.93463660971 0.01626926281 + -0.2551020408x + x2 = 0.93463660971 Factor a perfect square on the left side: (x + -0.1275510204)(x + -0.1275510204) = 0.93463660971 Calculate the square root of the right side: 0.966766057 Break this problem into two subproblems by setting (x + -0.1275510204) equal to 0.966766057 and -0.966766057.Subproblem 1
x + -0.1275510204 = 0.966766057 Simplifying x + -0.1275510204 = 0.966766057 Reorder the terms: -0.1275510204 + x = 0.966766057 Solving -0.1275510204 + x = 0.966766057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1275510204' to each side of the equation. -0.1275510204 + 0.1275510204 + x = 0.966766057 + 0.1275510204 Combine like terms: -0.1275510204 + 0.1275510204 = 0.0000000000 0.0000000000 + x = 0.966766057 + 0.1275510204 x = 0.966766057 + 0.1275510204 Combine like terms: 0.966766057 + 0.1275510204 = 1.0943170774 x = 1.0943170774 Simplifying x = 1.0943170774Subproblem 2
x + -0.1275510204 = -0.966766057 Simplifying x + -0.1275510204 = -0.966766057 Reorder the terms: -0.1275510204 + x = -0.966766057 Solving -0.1275510204 + x = -0.966766057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1275510204' to each side of the equation. -0.1275510204 + 0.1275510204 + x = -0.966766057 + 0.1275510204 Combine like terms: -0.1275510204 + 0.1275510204 = 0.0000000000 0.0000000000 + x = -0.966766057 + 0.1275510204 x = -0.966766057 + 0.1275510204 Combine like terms: -0.966766057 + 0.1275510204 = -0.8392150366 x = -0.8392150366 Simplifying x = -0.8392150366Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0943170774, -0.8392150366}
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