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Simplifying 35x2 + -45x + -4 = 0 Reorder the terms: -4 + -45x + 35x2 = 0 Solving -4 + -45x + 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'. -0.1142857143 + -1.285714286x + x2 = 0 Move the constant term to the right: Add '0.1142857143' to each side of the equation. -0.1142857143 + -1.285714286x + 0.1142857143 + x2 = 0 + 0.1142857143 Reorder the terms: -0.1142857143 + 0.1142857143 + -1.285714286x + x2 = 0 + 0.1142857143 Combine like terms: -0.1142857143 + 0.1142857143 = 0.0000000000 0.0000000000 + -1.285714286x + x2 = 0 + 0.1142857143 -1.285714286x + x2 = 0 + 0.1142857143 Combine like terms: 0 + 0.1142857143 = 0.1142857143 -1.285714286x + x2 = 0.1142857143 The x term is -1.285714286x. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286x + 0.4132653063 + x2 = 0.1142857143 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286x + x2 = 0.1142857143 + 0.4132653063 Combine like terms: 0.1142857143 + 0.4132653063 = 0.5275510206 0.4132653063 + -1.285714286x + x2 = 0.5275510206 Factor a perfect square on the left side: (x + -0.642857143)(x + -0.642857143) = 0.5275510206 Calculate the square root of the right side: 0.726327075 Break this problem into two subproblems by setting (x + -0.642857143) equal to 0.726327075 and -0.726327075.Subproblem 1
x + -0.642857143 = 0.726327075 Simplifying x + -0.642857143 = 0.726327075 Reorder the terms: -0.642857143 + x = 0.726327075 Solving -0.642857143 + x = 0.726327075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + x = 0.726327075 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = 0.726327075 + 0.642857143 x = 0.726327075 + 0.642857143 Combine like terms: 0.726327075 + 0.642857143 = 1.369184218 x = 1.369184218 Simplifying x = 1.369184218Subproblem 2
x + -0.642857143 = -0.726327075 Simplifying x + -0.642857143 = -0.726327075 Reorder the terms: -0.642857143 + x = -0.726327075 Solving -0.642857143 + x = -0.726327075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + x = -0.726327075 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = -0.726327075 + 0.642857143 x = -0.726327075 + 0.642857143 Combine like terms: -0.726327075 + 0.642857143 = -0.083469932 x = -0.083469932 Simplifying x = -0.083469932Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.369184218, -0.083469932}
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