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Simplifying 4.42x2 + -10.14x + 3.79 = 0 Reorder the terms: 3.79 + -10.14x + 4.42x2 = 0 Solving 3.79 + -10.14x + 4.42x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.42 the coefficient of the squared term: Divide each side by '4.42'. 0.8574660633 + -2.294117647x + x2 = 0 Move the constant term to the right: Add '-0.8574660633' to each side of the equation. 0.8574660633 + -2.294117647x + -0.8574660633 + x2 = 0 + -0.8574660633 Reorder the terms: 0.8574660633 + -0.8574660633 + -2.294117647x + x2 = 0 + -0.8574660633 Combine like terms: 0.8574660633 + -0.8574660633 = 0.0000000000 0.0000000000 + -2.294117647x + x2 = 0 + -0.8574660633 -2.294117647x + x2 = 0 + -0.8574660633 Combine like terms: 0 + -0.8574660633 = -0.8574660633 -2.294117647x + x2 = -0.8574660633 The x term is -2.294117647x. Take half its coefficient (-1.147058824). Square it (1.315743946) and add it to both sides. Add '1.315743946' to each side of the equation. -2.294117647x + 1.315743946 + x2 = -0.8574660633 + 1.315743946 Reorder the terms: 1.315743946 + -2.294117647x + x2 = -0.8574660633 + 1.315743946 Combine like terms: -0.8574660633 + 1.315743946 = 0.4582778827 1.315743946 + -2.294117647x + x2 = 0.4582778827 Factor a perfect square on the left side: (x + -1.147058824)(x + -1.147058824) = 0.4582778827 Calculate the square root of the right side: 0.676962246 Break this problem into two subproblems by setting (x + -1.147058824) equal to 0.676962246 and -0.676962246.Subproblem 1
x + -1.147058824 = 0.676962246 Simplifying x + -1.147058824 = 0.676962246 Reorder the terms: -1.147058824 + x = 0.676962246 Solving -1.147058824 + x = 0.676962246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.147058824' to each side of the equation. -1.147058824 + 1.147058824 + x = 0.676962246 + 1.147058824 Combine like terms: -1.147058824 + 1.147058824 = 0.000000000 0.000000000 + x = 0.676962246 + 1.147058824 x = 0.676962246 + 1.147058824 Combine like terms: 0.676962246 + 1.147058824 = 1.82402107 x = 1.82402107 Simplifying x = 1.82402107Subproblem 2
x + -1.147058824 = -0.676962246 Simplifying x + -1.147058824 = -0.676962246 Reorder the terms: -1.147058824 + x = -0.676962246 Solving -1.147058824 + x = -0.676962246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.147058824' to each side of the equation. -1.147058824 + 1.147058824 + x = -0.676962246 + 1.147058824 Combine like terms: -1.147058824 + 1.147058824 = 0.000000000 0.000000000 + x = -0.676962246 + 1.147058824 x = -0.676962246 + 1.147058824 Combine like terms: -0.676962246 + 1.147058824 = 0.470096578 x = 0.470096578 Simplifying x = 0.470096578Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.82402107, 0.470096578}
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