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Simplifying 20x2 + 7x + -7 = 0 Reorder the terms: -7 + 7x + 20x2 = 0 Solving -7 + 7x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.35 + 0.35x + x2 = 0 Move the constant term to the right: Add '0.35' to each side of the equation. -0.35 + 0.35x + 0.35 + x2 = 0 + 0.35 Reorder the terms: -0.35 + 0.35 + 0.35x + x2 = 0 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + 0.35x + x2 = 0 + 0.35 0.35x + x2 = 0 + 0.35 Combine like terms: 0 + 0.35 = 0.35 0.35x + x2 = 0.35 The x term is 0.35x. Take half its coefficient (0.175). Square it (0.030625) and add it to both sides. Add '0.030625' to each side of the equation. 0.35x + 0.030625 + x2 = 0.35 + 0.030625 Reorder the terms: 0.030625 + 0.35x + x2 = 0.35 + 0.030625 Combine like terms: 0.35 + 0.030625 = 0.380625 0.030625 + 0.35x + x2 = 0.380625 Factor a perfect square on the left side: (x + 0.175)(x + 0.175) = 0.380625 Calculate the square root of the right side: 0.616948134 Break this problem into two subproblems by setting (x + 0.175) equal to 0.616948134 and -0.616948134.Subproblem 1
x + 0.175 = 0.616948134 Simplifying x + 0.175 = 0.616948134 Reorder the terms: 0.175 + x = 0.616948134 Solving 0.175 + x = 0.616948134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.175' to each side of the equation. 0.175 + -0.175 + x = 0.616948134 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + x = 0.616948134 + -0.175 x = 0.616948134 + -0.175 Combine like terms: 0.616948134 + -0.175 = 0.441948134 x = 0.441948134 Simplifying x = 0.441948134Subproblem 2
x + 0.175 = -0.616948134 Simplifying x + 0.175 = -0.616948134 Reorder the terms: 0.175 + x = -0.616948134 Solving 0.175 + x = -0.616948134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.175' to each side of the equation. 0.175 + -0.175 + x = -0.616948134 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + x = -0.616948134 + -0.175 x = -0.616948134 + -0.175 Combine like terms: -0.616948134 + -0.175 = -0.791948134 x = -0.791948134 Simplifying x = -0.791948134Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.441948134, -0.791948134}
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