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Simplifying 0 = 165 + 65.96x + -4.9x2 Solving 0 = 165 + 65.96x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -165 = -165 -165 + -65.96x + 4.9x2 = 165 + 65.96x + -4.9x2 + -165 + -65.96x + 4.9x2 Reorder the terms: -165 + -65.96x + 4.9x2 = 165 + -165 + 65.96x + -65.96x + -4.9x2 + 4.9x2 Combine like terms: 165 + -165 = 0 -165 + -65.96x + 4.9x2 = 0 + 65.96x + -65.96x + -4.9x2 + 4.9x2 -165 + -65.96x + 4.9x2 = 65.96x + -65.96x + -4.9x2 + 4.9x2 Combine like terms: 65.96x + -65.96x = 0.00 -165 + -65.96x + 4.9x2 = 0.00 + -4.9x2 + 4.9x2 -165 + -65.96x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -165 + -65.96x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -33.67346939 + -13.46122449x + x2 = 0 Move the constant term to the right: Add '33.67346939' to each side of the equation. -33.67346939 + -13.46122449x + 33.67346939 + x2 = 0 + 33.67346939 Reorder the terms: -33.67346939 + 33.67346939 + -13.46122449x + x2 = 0 + 33.67346939 Combine like terms: -33.67346939 + 33.67346939 = 0.00000000 0.00000000 + -13.46122449x + x2 = 0 + 33.67346939 -13.46122449x + x2 = 0 + 33.67346939 Combine like terms: 0 + 33.67346939 = 33.67346939 -13.46122449x + x2 = 33.67346939 The x term is -13.46122449x. Take half its coefficient (-6.730612245). Square it (45.30114119) and add it to both sides. Add '45.30114119' to each side of the equation. -13.46122449x + 45.30114119 + x2 = 33.67346939 + 45.30114119 Reorder the terms: 45.30114119 + -13.46122449x + x2 = 33.67346939 + 45.30114119 Combine like terms: 33.67346939 + 45.30114119 = 78.97461058 45.30114119 + -13.46122449x + x2 = 78.97461058 Factor a perfect square on the left side: (x + -6.730612245)(x + -6.730612245) = 78.97461058 Calculate the square root of the right side: 8.886766036 Break this problem into two subproblems by setting (x + -6.730612245) equal to 8.886766036 and -8.886766036.Subproblem 1
x + -6.730612245 = 8.886766036 Simplifying x + -6.730612245 = 8.886766036 Reorder the terms: -6.730612245 + x = 8.886766036 Solving -6.730612245 + x = 8.886766036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.730612245' to each side of the equation. -6.730612245 + 6.730612245 + x = 8.886766036 + 6.730612245 Combine like terms: -6.730612245 + 6.730612245 = 0.000000000 0.000000000 + x = 8.886766036 + 6.730612245 x = 8.886766036 + 6.730612245 Combine like terms: 8.886766036 + 6.730612245 = 15.617378281 x = 15.617378281 Simplifying x = 15.617378281Subproblem 2
x + -6.730612245 = -8.886766036 Simplifying x + -6.730612245 = -8.886766036 Reorder the terms: -6.730612245 + x = -8.886766036 Solving -6.730612245 + x = -8.886766036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.730612245' to each side of the equation. -6.730612245 + 6.730612245 + x = -8.886766036 + 6.730612245 Combine like terms: -6.730612245 + 6.730612245 = 0.000000000 0.000000000 + x = -8.886766036 + 6.730612245 x = -8.886766036 + 6.730612245 Combine like terms: -8.886766036 + 6.730612245 = -2.156153791 x = -2.156153791 Simplifying x = -2.156153791Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.617378281, -2.156153791}
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