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Simplifying -350x2 + 325x + 550 = 0 Reorder the terms: 550 + 325x + -350x2 = 0 Solving 550 + 325x + -350x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '25'. 25(22 + 13x + -14x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(22 + 13x + -14x2)' equal to zero and attempt to solve: Simplifying 22 + 13x + -14x2 = 0 Solving 22 + 13x + -14x2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -1.571428571 + -0.9285714286x + x2 = 0 Move the constant term to the right: Add '1.571428571' to each side of the equation. -1.571428571 + -0.9285714286x + 1.571428571 + x2 = 0 + 1.571428571 Reorder the terms: -1.571428571 + 1.571428571 + -0.9285714286x + x2 = 0 + 1.571428571 Combine like terms: -1.571428571 + 1.571428571 = 0.000000000 0.000000000 + -0.9285714286x + x2 = 0 + 1.571428571 -0.9285714286x + x2 = 0 + 1.571428571 Combine like terms: 0 + 1.571428571 = 1.571428571 -0.9285714286x + x2 = 1.571428571 The x term is -0.9285714286x. Take half its coefficient (-0.4642857143). Square it (0.2155612245) and add it to both sides. Add '0.2155612245' to each side of the equation. -0.9285714286x + 0.2155612245 + x2 = 1.571428571 + 0.2155612245 Reorder the terms: 0.2155612245 + -0.9285714286x + x2 = 1.571428571 + 0.2155612245 Combine like terms: 1.571428571 + 0.2155612245 = 1.7869897955 0.2155612245 + -0.9285714286x + x2 = 1.7869897955 Factor a perfect square on the left side: (x + -0.4642857143)(x + -0.4642857143) = 1.7869897955 Calculate the square root of the right side: 1.336783376 Break this problem into two subproblems by setting (x + -0.4642857143) equal to 1.336783376 and -1.336783376.Subproblem 1
x + -0.4642857143 = 1.336783376 Simplifying x + -0.4642857143 = 1.336783376 Reorder the terms: -0.4642857143 + x = 1.336783376 Solving -0.4642857143 + x = 1.336783376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4642857143' to each side of the equation. -0.4642857143 + 0.4642857143 + x = 1.336783376 + 0.4642857143 Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000 0.0000000000 + x = 1.336783376 + 0.4642857143 x = 1.336783376 + 0.4642857143 Combine like terms: 1.336783376 + 0.4642857143 = 1.8010690903 x = 1.8010690903 Simplifying x = 1.8010690903Subproblem 2
x + -0.4642857143 = -1.336783376 Simplifying x + -0.4642857143 = -1.336783376 Reorder the terms: -0.4642857143 + x = -1.336783376 Solving -0.4642857143 + x = -1.336783376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4642857143' to each side of the equation. -0.4642857143 + 0.4642857143 + x = -1.336783376 + 0.4642857143 Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000 0.0000000000 + x = -1.336783376 + 0.4642857143 x = -1.336783376 + 0.4642857143 Combine like terms: -1.336783376 + 0.4642857143 = -0.8724976617 x = -0.8724976617 Simplifying x = -0.8724976617Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8010690903, -0.8724976617}Solution
x = {1.8010690903, -0.8724976617}
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