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Simplifying 5x2 + 49x + 112 = 0 Reorder the terms: 112 + 49x + 5x2 = 0 Solving 112 + 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'. 22.4 + 9.8x + x2 = 0 Move the constant term to the right: Add '-22.4' to each side of the equation. 22.4 + 9.8x + -22.4 + x2 = 0 + -22.4 Reorder the terms: 22.4 + -22.4 + 9.8x + x2 = 0 + -22.4 Combine like terms: 22.4 + -22.4 = 0.0 0.0 + 9.8x + x2 = 0 + -22.4 9.8x + x2 = 0 + -22.4 Combine like terms: 0 + -22.4 = -22.4 9.8x + x2 = -22.4 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 = -22.4 + 24.01 Reorder the terms: 24.01 + 9.8x + x2 = -22.4 + 24.01 Combine like terms: -22.4 + 24.01 = 1.61 24.01 + 9.8x + x2 = 1.61 Factor a perfect square on the left side: (x + 4.9)(x + 4.9) = 1.61 Calculate the square root of the right side: 1.268857754 Break this problem into two subproblems by setting (x + 4.9) equal to 1.268857754 and -1.268857754.Subproblem 1
x + 4.9 = 1.268857754 Simplifying x + 4.9 = 1.268857754 Reorder the terms: 4.9 + x = 1.268857754 Solving 4.9 + x = 1.268857754 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 = 1.268857754 + -4.9 Combine like terms: 4.9 + -4.9 = 0.0 0.0 + x = 1.268857754 + -4.9 x = 1.268857754 + -4.9 Combine like terms: 1.268857754 + -4.9 = -3.631142246 x = -3.631142246 Simplifying x = -3.631142246Subproblem 2
x + 4.9 = -1.268857754 Simplifying x + 4.9 = -1.268857754 Reorder the terms: 4.9 + x = -1.268857754 Solving 4.9 + x = -1.268857754 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 = -1.268857754 + -4.9 Combine like terms: 4.9 + -4.9 = 0.0 0.0 + x = -1.268857754 + -4.9 x = -1.268857754 + -4.9 Combine like terms: -1.268857754 + -4.9 = -6.168857754 x = -6.168857754 Simplifying x = -6.168857754Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.631142246, -6.168857754}
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