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Simplifying -5.6x2 + 117x + 1280 = 0 Reorder the terms: 1280 + 117x + -5.6x2 = 0 Solving 1280 + 117x + -5.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5.6 the coefficient of the squared term: Divide each side by '-5.6'. -228.5714286 + -20.89285714x + x2 = 0 Move the constant term to the right: Add '228.5714286' to each side of the equation. -228.5714286 + -20.89285714x + 228.5714286 + x2 = 0 + 228.5714286 Reorder the terms: -228.5714286 + 228.5714286 + -20.89285714x + x2 = 0 + 228.5714286 Combine like terms: -228.5714286 + 228.5714286 = 0.0000000 0.0000000 + -20.89285714x + x2 = 0 + 228.5714286 -20.89285714x + x2 = 0 + 228.5714286 Combine like terms: 0 + 228.5714286 = 228.5714286 -20.89285714x + x2 = 228.5714286 The x term is -20.89285714x. Take half its coefficient (-10.44642857). Square it (109.1278699) and add it to both sides. Add '109.1278699' to each side of the equation. -20.89285714x + 109.1278699 + x2 = 228.5714286 + 109.1278699 Reorder the terms: 109.1278699 + -20.89285714x + x2 = 228.5714286 + 109.1278699 Combine like terms: 228.5714286 + 109.1278699 = 337.6992985 109.1278699 + -20.89285714x + x2 = 337.6992985 Factor a perfect square on the left side: (x + -10.44642857)(x + -10.44642857) = 337.6992985 Calculate the square root of the right side: 18.376596488 Break this problem into two subproblems by setting (x + -10.44642857) equal to 18.376596488 and -18.376596488.Subproblem 1
x + -10.44642857 = 18.376596488 Simplifying x + -10.44642857 = 18.376596488 Reorder the terms: -10.44642857 + x = 18.376596488 Solving -10.44642857 + x = 18.376596488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.44642857' to each side of the equation. -10.44642857 + 10.44642857 + x = 18.376596488 + 10.44642857 Combine like terms: -10.44642857 + 10.44642857 = 0.00000000 0.00000000 + x = 18.376596488 + 10.44642857 x = 18.376596488 + 10.44642857 Combine like terms: 18.376596488 + 10.44642857 = 28.823025058 x = 28.823025058 Simplifying x = 28.823025058Subproblem 2
x + -10.44642857 = -18.376596488 Simplifying x + -10.44642857 = -18.376596488 Reorder the terms: -10.44642857 + x = -18.376596488 Solving -10.44642857 + x = -18.376596488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.44642857' to each side of the equation. -10.44642857 + 10.44642857 + x = -18.376596488 + 10.44642857 Combine like terms: -10.44642857 + 10.44642857 = 0.00000000 0.00000000 + x = -18.376596488 + 10.44642857 x = -18.376596488 + 10.44642857 Combine like terms: -18.376596488 + 10.44642857 = -7.930167918 x = -7.930167918 Simplifying x = -7.930167918Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.823025058, -7.930167918}
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