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Simplifying 28x2 + -15x + -32 = 0 Reorder the terms: -32 + -15x + 28x2 = 0 Solving -32 + -15x + 28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -1.142857143 + -0.5357142857x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -0.5357142857x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -0.5357142857x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -0.5357142857x + x2 = 0 + 1.142857143 -0.5357142857x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -0.5357142857x + x2 = 1.142857143 The x term is -0.5357142857x. Take half its coefficient (-0.2678571429). Square it (0.07174744900) and add it to both sides. Add '0.07174744900' to each side of the equation. -0.5357142857x + 0.07174744900 + x2 = 1.142857143 + 0.07174744900 Reorder the terms: 0.07174744900 + -0.5357142857x + x2 = 1.142857143 + 0.07174744900 Combine like terms: 1.142857143 + 0.07174744900 = 1.214604592 0.07174744900 + -0.5357142857x + x2 = 1.214604592 Factor a perfect square on the left side: (x + -0.2678571429)(x + -0.2678571429) = 1.214604592 Calculate the square root of the right side: 1.102091009 Break this problem into two subproblems by setting (x + -0.2678571429) equal to 1.102091009 and -1.102091009.Subproblem 1
x + -0.2678571429 = 1.102091009 Simplifying x + -0.2678571429 = 1.102091009 Reorder the terms: -0.2678571429 + x = 1.102091009 Solving -0.2678571429 + x = 1.102091009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2678571429' to each side of the equation. -0.2678571429 + 0.2678571429 + x = 1.102091009 + 0.2678571429 Combine like terms: -0.2678571429 + 0.2678571429 = 0.0000000000 0.0000000000 + x = 1.102091009 + 0.2678571429 x = 1.102091009 + 0.2678571429 Combine like terms: 1.102091009 + 0.2678571429 = 1.3699481519 x = 1.3699481519 Simplifying x = 1.3699481519Subproblem 2
x + -0.2678571429 = -1.102091009 Simplifying x + -0.2678571429 = -1.102091009 Reorder the terms: -0.2678571429 + x = -1.102091009 Solving -0.2678571429 + x = -1.102091009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2678571429' to each side of the equation. -0.2678571429 + 0.2678571429 + x = -1.102091009 + 0.2678571429 Combine like terms: -0.2678571429 + 0.2678571429 = 0.0000000000 0.0000000000 + x = -1.102091009 + 0.2678571429 x = -1.102091009 + 0.2678571429 Combine like terms: -1.102091009 + 0.2678571429 = -0.8342338661 x = -0.8342338661 Simplifying x = -0.8342338661Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3699481519, -0.8342338661}
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