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Simplifying 5x2 = 35x + -3 Reorder the terms: 5x2 = -3 + 35x Solving 5x2 = -3 + 35x Solving for variable 'x'. Reorder the terms: 3 + -35x + 5x2 = -3 + 35x + 3 + -35x Reorder the terms: 3 + -35x + 5x2 = -3 + 3 + 35x + -35x Combine like terms: -3 + 3 = 0 3 + -35x + 5x2 = 0 + 35x + -35x 3 + -35x + 5x2 = 35x + -35x Combine like terms: 35x + -35x = 0 3 + -35x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + -7x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -7x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -7x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -7x + x2 = 0 + -0.6 -7x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -7x + x2 = -0.6 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -0.6 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -0.6 + 12.25 Combine like terms: -0.6 + 12.25 = 11.65 12.25 + -7x + x2 = 11.65 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 11.65 Calculate the square root of the right side: 3.413209633 Break this problem into two subproblems by setting (x + -3.5) equal to 3.413209633 and -3.413209633.Subproblem 1
x + -3.5 = 3.413209633 Simplifying x + -3.5 = 3.413209633 Reorder the terms: -3.5 + x = 3.413209633 Solving -3.5 + x = 3.413209633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.413209633 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.413209633 + 3.5 x = 3.413209633 + 3.5 Combine like terms: 3.413209633 + 3.5 = 6.913209633 x = 6.913209633 Simplifying x = 6.913209633Subproblem 2
x + -3.5 = -3.413209633 Simplifying x + -3.5 = -3.413209633 Reorder the terms: -3.5 + x = -3.413209633 Solving -3.5 + x = -3.413209633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.413209633 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.413209633 + 3.5 x = -3.413209633 + 3.5 Combine like terms: -3.413209633 + 3.5 = 0.086790367 x = 0.086790367 Simplifying x = 0.086790367Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.913209633, 0.086790367}
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