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Simplifying 2.4x2 + -3.5x = 2.2 Reorder the terms: -3.5x + 2.4x2 = 2.2 Solving -3.5x + 2.4x2 = 2.2 Solving for variable 'x'. Reorder the terms: -2.2 + -3.5x + 2.4x2 = 2.2 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 -2.2 + -3.5x + 2.4x2 = 0.0 Begin completing the square. Divide all terms by 2.4 the coefficient of the squared term: Divide each side by '2.4'. -0.9166666667 + -1.458333333x + x2 = 0 Move the constant term to the right: Add '0.9166666667' to each side of the equation. -0.9166666667 + -1.458333333x + 0.9166666667 + x2 = 0 + 0.9166666667 Reorder the terms: -0.9166666667 + 0.9166666667 + -1.458333333x + x2 = 0 + 0.9166666667 Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000 0.0000000000 + -1.458333333x + x2 = 0 + 0.9166666667 -1.458333333x + x2 = 0 + 0.9166666667 Combine like terms: 0 + 0.9166666667 = 0.9166666667 -1.458333333x + x2 = 0.9166666667 The x term is -1.458333333x. Take half its coefficient (-0.7291666665). Square it (0.5316840275) and add it to both sides. Add '0.5316840275' to each side of the equation. -1.458333333x + 0.5316840275 + x2 = 0.9166666667 + 0.5316840275 Reorder the terms: 0.5316840275 + -1.458333333x + x2 = 0.9166666667 + 0.5316840275 Combine like terms: 0.9166666667 + 0.5316840275 = 1.4483506942 0.5316840275 + -1.458333333x + x2 = 1.4483506942 Factor a perfect square on the left side: (x + -0.7291666665)(x + -0.7291666665) = 1.4483506942 Calculate the square root of the right side: 1.203474426 Break this problem into two subproblems by setting (x + -0.7291666665) equal to 1.203474426 and -1.203474426.Subproblem 1
x + -0.7291666665 = 1.203474426 Simplifying x + -0.7291666665 = 1.203474426 Reorder the terms: -0.7291666665 + x = 1.203474426 Solving -0.7291666665 + x = 1.203474426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7291666665' to each side of the equation. -0.7291666665 + 0.7291666665 + x = 1.203474426 + 0.7291666665 Combine like terms: -0.7291666665 + 0.7291666665 = 0.0000000000 0.0000000000 + x = 1.203474426 + 0.7291666665 x = 1.203474426 + 0.7291666665 Combine like terms: 1.203474426 + 0.7291666665 = 1.9326410925 x = 1.9326410925 Simplifying x = 1.9326410925Subproblem 2
x + -0.7291666665 = -1.203474426 Simplifying x + -0.7291666665 = -1.203474426 Reorder the terms: -0.7291666665 + x = -1.203474426 Solving -0.7291666665 + x = -1.203474426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7291666665' to each side of the equation. -0.7291666665 + 0.7291666665 + x = -1.203474426 + 0.7291666665 Combine like terms: -0.7291666665 + 0.7291666665 = 0.0000000000 0.0000000000 + x = -1.203474426 + 0.7291666665 x = -1.203474426 + 0.7291666665 Combine like terms: -1.203474426 + 0.7291666665 = -0.4743077595 x = -0.4743077595 Simplifying x = -0.4743077595Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9326410925, -0.4743077595}
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