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Simplifying 5x2 + 8x + -220 = 0 Reorder the terms: -220 + 8x + 5x2 = 0 Solving -220 + 8x + 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'. -44 + 1.6x + x2 = 0 Move the constant term to the right: Add '44' to each side of the equation. -44 + 1.6x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + 1.6x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 1.6x + x2 = 0 + 44 1.6x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 1.6x + x2 = 44 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 = 44 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 44 + 0.64 Combine like terms: 44 + 0.64 = 44.64 0.64 + 1.6x + x2 = 44.64 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 44.64 Calculate the square root of the right side: 6.681317235 Break this problem into two subproblems by setting (x + 0.8) equal to 6.681317235 and -6.681317235.Subproblem 1
x + 0.8 = 6.681317235 Simplifying x + 0.8 = 6.681317235 Reorder the terms: 0.8 + x = 6.681317235 Solving 0.8 + x = 6.681317235 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 = 6.681317235 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 6.681317235 + -0.8 x = 6.681317235 + -0.8 Combine like terms: 6.681317235 + -0.8 = 5.881317235 x = 5.881317235 Simplifying x = 5.881317235Subproblem 2
x + 0.8 = -6.681317235 Simplifying x + 0.8 = -6.681317235 Reorder the terms: 0.8 + x = -6.681317235 Solving 0.8 + x = -6.681317235 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 = -6.681317235 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -6.681317235 + -0.8 x = -6.681317235 + -0.8 Combine like terms: -6.681317235 + -0.8 = -7.481317235 x = -7.481317235 Simplifying x = -7.481317235Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.881317235, -7.481317235}
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