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Simplifying 5x2 + -35x + -7 = 0 Reorder the terms: -7 + -35x + 5x2 = 0 Solving -7 + -35x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -7x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -7x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -7x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -7x + x2 = 0 + 1.4 -7x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -7x + x2 = 1.4 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 = 1.4 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 1.4 + 12.25 Combine like terms: 1.4 + 12.25 = 13.65 12.25 + -7x + x2 = 13.65 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 13.65 Calculate the square root of the right side: 3.69459064 Break this problem into two subproblems by setting (x + -3.5) equal to 3.69459064 and -3.69459064.Subproblem 1
x + -3.5 = 3.69459064 Simplifying x + -3.5 = 3.69459064 Reorder the terms: -3.5 + x = 3.69459064 Solving -3.5 + x = 3.69459064 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 = 3.69459064 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.69459064 + 3.5 x = 3.69459064 + 3.5 Combine like terms: 3.69459064 + 3.5 = 7.19459064 x = 7.19459064 Simplifying x = 7.19459064Subproblem 2
x + -3.5 = -3.69459064 Simplifying x + -3.5 = -3.69459064 Reorder the terms: -3.5 + x = -3.69459064 Solving -3.5 + x = -3.69459064 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 = -3.69459064 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.69459064 + 3.5 x = -3.69459064 + 3.5 Combine like terms: -3.69459064 + 3.5 = -0.19459064 x = -0.19459064 Simplifying x = -0.19459064Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.19459064, -0.19459064}
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