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Simplifying 5x2 + 8x + -64 = 180 Reorder the terms: -64 + 8x + 5x2 = 180 Solving -64 + 8x + 5x2 = 180 Solving for variable 'x'. Reorder the terms: -64 + -180 + 8x + 5x2 = 180 + -180 Combine like terms: -64 + -180 = -244 -244 + 8x + 5x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -244 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -48.8 + 1.6x + x2 = 0 Move the constant term to the right: Add '48.8' to each side of the equation. -48.8 + 1.6x + 48.8 + x2 = 0 + 48.8 Reorder the terms: -48.8 + 48.8 + 1.6x + x2 = 0 + 48.8 Combine like terms: -48.8 + 48.8 = 0.0 0.0 + 1.6x + x2 = 0 + 48.8 1.6x + x2 = 0 + 48.8 Combine like terms: 0 + 48.8 = 48.8 1.6x + x2 = 48.8 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 48.8 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 48.8 + 0.64 Combine like terms: 48.8 + 0.64 = 49.44 0.64 + 1.6x + x2 = 49.44 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 49.44 Calculate the square root of the right side: 7.031358332 Break this problem into two subproblems by setting (x + 0.8) equal to 7.031358332 and -7.031358332.Subproblem 1
x + 0.8 = 7.031358332 Simplifying x + 0.8 = 7.031358332 Reorder the terms: 0.8 + x = 7.031358332 Solving 0.8 + x = 7.031358332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 7.031358332 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 7.031358332 + -0.8 x = 7.031358332 + -0.8 Combine like terms: 7.031358332 + -0.8 = 6.231358332 x = 6.231358332 Simplifying x = 6.231358332Subproblem 2
x + 0.8 = -7.031358332 Simplifying x + 0.8 = -7.031358332 Reorder the terms: 0.8 + x = -7.031358332 Solving 0.8 + x = -7.031358332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -7.031358332 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -7.031358332 + -0.8 x = -7.031358332 + -0.8 Combine like terms: -7.031358332 + -0.8 = -7.831358332 x = -7.831358332 Simplifying x = -7.831358332Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.231358332, -7.831358332}
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