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Simplifying 35x2 + 15x + -68 = 0 Reorder the terms: -68 + 15x + 35x2 = 0 Solving -68 + 15x + 35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -1.942857143 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '1.942857143' to each side of the equation. -1.942857143 + 0.4285714286x + 1.942857143 + x2 = 0 + 1.942857143 Reorder the terms: -1.942857143 + 1.942857143 + 0.4285714286x + x2 = 0 + 1.942857143 Combine like terms: -1.942857143 + 1.942857143 = 0.000000000 0.000000000 + 0.4285714286x + x2 = 0 + 1.942857143 0.4285714286x + x2 = 0 + 1.942857143 Combine like terms: 0 + 1.942857143 = 1.942857143 0.4285714286x + x2 = 1.942857143 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = 1.942857143 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 1.942857143 + 0.04591836735 Combine like terms: 1.942857143 + 0.04591836735 = 1.98877551035 0.04591836735 + 0.4285714286x + x2 = 1.98877551035 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 1.98877551035 Calculate the square root of the right side: 1.410239522 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 1.410239522 and -1.410239522.Subproblem 1
x + 0.2142857143 = 1.410239522 Simplifying x + 0.2142857143 = 1.410239522 Reorder the terms: 0.2142857143 + x = 1.410239522 Solving 0.2142857143 + x = 1.410239522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = 1.410239522 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 1.410239522 + -0.2142857143 x = 1.410239522 + -0.2142857143 Combine like terms: 1.410239522 + -0.2142857143 = 1.1959538077 x = 1.1959538077 Simplifying x = 1.1959538077Subproblem 2
x + 0.2142857143 = -1.410239522 Simplifying x + 0.2142857143 = -1.410239522 Reorder the terms: 0.2142857143 + x = -1.410239522 Solving 0.2142857143 + x = -1.410239522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = -1.410239522 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -1.410239522 + -0.2142857143 x = -1.410239522 + -0.2142857143 Combine like terms: -1.410239522 + -0.2142857143 = -1.6245252363 x = -1.6245252363 Simplifying x = -1.6245252363Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1959538077, -1.6245252363}
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