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Simplifying -0.05x2 + 7.3x + 235 = 303 Reorder the terms: 235 + 7.3x + -0.05x2 = 303 Solving 235 + 7.3x + -0.05x2 = 303 Solving for variable 'x'. Reorder the terms: 235 + -303 + 7.3x + -0.05x2 = 303 + -303 Combine like terms: 235 + -303 = -68 -68 + 7.3x + -0.05x2 = 303 + -303 Combine like terms: 303 + -303 = 0 -68 + 7.3x + -0.05x2 = 0 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. 1360 + -146x + x2 = 0 Move the constant term to the right: Add '-1360' to each side of the equation. 1360 + -146x + -1360 + x2 = 0 + -1360 Reorder the terms: 1360 + -1360 + -146x + x2 = 0 + -1360 Combine like terms: 1360 + -1360 = 0 0 + -146x + x2 = 0 + -1360 -146x + x2 = 0 + -1360 Combine like terms: 0 + -1360 = -1360 -146x + x2 = -1360 The x term is -146x. Take half its coefficient (-73). Square it (5329) and add it to both sides. Add '5329' to each side of the equation. -146x + 5329 + x2 = -1360 + 5329 Reorder the terms: 5329 + -146x + x2 = -1360 + 5329 Combine like terms: -1360 + 5329 = 3969 5329 + -146x + x2 = 3969 Factor a perfect square on the left side: (x + -73)(x + -73) = 3969 Calculate the square root of the right side: 63 Break this problem into two subproblems by setting (x + -73) equal to 63 and -63.Subproblem 1
x + -73 = 63 Simplifying x + -73 = 63 Reorder the terms: -73 + x = 63 Solving -73 + x = 63 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '73' to each side of the equation. -73 + 73 + x = 63 + 73 Combine like terms: -73 + 73 = 0 0 + x = 63 + 73 x = 63 + 73 Combine like terms: 63 + 73 = 136 x = 136 Simplifying x = 136Subproblem 2
x + -73 = -63 Simplifying x + -73 = -63 Reorder the terms: -73 + x = -63 Solving -73 + x = -63 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '73' to each side of the equation. -73 + 73 + x = -63 + 73 Combine like terms: -73 + 73 = 0 0 + x = -63 + 73 x = -63 + 73 Combine like terms: -63 + 73 = 10 x = 10 Simplifying x = 10Solution
The solution to the problem is based on the solutions from the subproblems. x = {136, 10}
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