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Simplifying 5x2 + -49x + -24 = 0 Reorder the terms: -24 + -49x + 5x2 = 0 Solving -24 + -49x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.8 + -9.8x + x2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + -9.8x + 4.8 + x2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + -9.8x + x2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + -9.8x + x2 = 0 + 4.8 -9.8x + x2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 -9.8x + x2 = 4.8 The x term is -9.8x. Take half its coefficient (-4.9). Square it (24.01) and add it to both sides. Add '24.01' to each side of the equation. -9.8x + 24.01 + x2 = 4.8 + 24.01 Reorder the terms: 24.01 + -9.8x + x2 = 4.8 + 24.01 Combine like terms: 4.8 + 24.01 = 28.81 24.01 + -9.8x + x2 = 28.81 Factor a perfect square on the left side: (x + -4.9)(x + -4.9) = 28.81 Calculate the square root of the right side: 5.36749476 Break this problem into two subproblems by setting (x + -4.9) equal to 5.36749476 and -5.36749476.Subproblem 1
x + -4.9 = 5.36749476 Simplifying x + -4.9 = 5.36749476 Reorder the terms: -4.9 + x = 5.36749476 Solving -4.9 + x = 5.36749476 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.9' to each side of the equation. -4.9 + 4.9 + x = 5.36749476 + 4.9 Combine like terms: -4.9 + 4.9 = 0.0 0.0 + x = 5.36749476 + 4.9 x = 5.36749476 + 4.9 Combine like terms: 5.36749476 + 4.9 = 10.26749476 x = 10.26749476 Simplifying x = 10.26749476Subproblem 2
x + -4.9 = -5.36749476 Simplifying x + -4.9 = -5.36749476 Reorder the terms: -4.9 + x = -5.36749476 Solving -4.9 + x = -5.36749476 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.9' to each side of the equation. -4.9 + 4.9 + x = -5.36749476 + 4.9 Combine like terms: -4.9 + 4.9 = 0.0 0.0 + x = -5.36749476 + 4.9 x = -5.36749476 + 4.9 Combine like terms: -5.36749476 + 4.9 = -0.46749476 x = -0.46749476 Simplifying x = -0.46749476Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.26749476, -0.46749476}
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