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Simplifying 5x2 + 56x + -480 = 0 Reorder the terms: -480 + 56x + 5x2 = 0 Solving -480 + 56x + 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'. -96 + 11.2x + x2 = 0 Move the constant term to the right: Add '96' to each side of the equation. -96 + 11.2x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + 11.2x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 11.2x + x2 = 0 + 96 11.2x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 11.2x + x2 = 96 The x term is 11.2x. Take half its coefficient (5.6). Square it (31.36) and add it to both sides. Add '31.36' to each side of the equation. 11.2x + 31.36 + x2 = 96 + 31.36 Reorder the terms: 31.36 + 11.2x + x2 = 96 + 31.36 Combine like terms: 96 + 31.36 = 127.36 31.36 + 11.2x + x2 = 127.36 Factor a perfect square on the left side: (x + 5.6)(x + 5.6) = 127.36 Calculate the square root of the right side: 11.285388784 Break this problem into two subproblems by setting (x + 5.6) equal to 11.285388784 and -11.285388784.Subproblem 1
x + 5.6 = 11.285388784 Simplifying x + 5.6 = 11.285388784 Reorder the terms: 5.6 + x = 11.285388784 Solving 5.6 + x = 11.285388784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.6' to each side of the equation. 5.6 + -5.6 + x = 11.285388784 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + x = 11.285388784 + -5.6 x = 11.285388784 + -5.6 Combine like terms: 11.285388784 + -5.6 = 5.685388784 x = 5.685388784 Simplifying x = 5.685388784Subproblem 2
x + 5.6 = -11.285388784 Simplifying x + 5.6 = -11.285388784 Reorder the terms: 5.6 + x = -11.285388784 Solving 5.6 + x = -11.285388784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.6' to each side of the equation. 5.6 + -5.6 + x = -11.285388784 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + x = -11.285388784 + -5.6 x = -11.285388784 + -5.6 Combine like terms: -11.285388784 + -5.6 = -16.885388784 x = -16.885388784 Simplifying x = -16.885388784Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.685388784, -16.885388784}
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