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Simplifying 35x2 + -190x + 168 = -8x + 1 Reorder the terms: 168 + -190x + 35x2 = -8x + 1 Reorder the terms: 168 + -190x + 35x2 = 1 + -8x Solving 168 + -190x + 35x2 = 1 + -8x Solving for variable 'x'. Reorder the terms: 168 + -1 + -190x + 8x + 35x2 = 1 + -8x + -1 + 8x Combine like terms: 168 + -1 = 167 167 + -190x + 8x + 35x2 = 1 + -8x + -1 + 8x Combine like terms: -190x + 8x = -182x 167 + -182x + 35x2 = 1 + -8x + -1 + 8x Reorder the terms: 167 + -182x + 35x2 = 1 + -1 + -8x + 8x Combine like terms: 1 + -1 = 0 167 + -182x + 35x2 = 0 + -8x + 8x 167 + -182x + 35x2 = -8x + 8x Combine like terms: -8x + 8x = 0 167 + -182x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. 4.771428571 + -5.2x + x2 = 0 Move the constant term to the right: Add '-4.771428571' to each side of the equation. 4.771428571 + -5.2x + -4.771428571 + x2 = 0 + -4.771428571 Reorder the terms: 4.771428571 + -4.771428571 + -5.2x + x2 = 0 + -4.771428571 Combine like terms: 4.771428571 + -4.771428571 = 0.000000000 0.000000000 + -5.2x + x2 = 0 + -4.771428571 -5.2x + x2 = 0 + -4.771428571 Combine like terms: 0 + -4.771428571 = -4.771428571 -5.2x + x2 = -4.771428571 The x term is -5.2x. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2x + 6.76 + x2 = -4.771428571 + 6.76 Reorder the terms: 6.76 + -5.2x + x2 = -4.771428571 + 6.76 Combine like terms: -4.771428571 + 6.76 = 1.988571429 6.76 + -5.2x + x2 = 1.988571429 Factor a perfect square on the left side: (x + -2.6)(x + -2.6) = 1.988571429 Calculate the square root of the right side: 1.410167163 Break this problem into two subproblems by setting (x + -2.6) equal to 1.410167163 and -1.410167163.Subproblem 1
x + -2.6 = 1.410167163 Simplifying x + -2.6 = 1.410167163 Reorder the terms: -2.6 + x = 1.410167163 Solving -2.6 + x = 1.410167163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = 1.410167163 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = 1.410167163 + 2.6 x = 1.410167163 + 2.6 Combine like terms: 1.410167163 + 2.6 = 4.010167163 x = 4.010167163 Simplifying x = 4.010167163Subproblem 2
x + -2.6 = -1.410167163 Simplifying x + -2.6 = -1.410167163 Reorder the terms: -2.6 + x = -1.410167163 Solving -2.6 + x = -1.410167163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = -1.410167163 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = -1.410167163 + 2.6 x = -1.410167163 + 2.6 Combine like terms: -1.410167163 + 2.6 = 1.189832837 x = 1.189832837 Simplifying x = 1.189832837Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.010167163, 1.189832837}
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