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Simplifying 3x + -7 = 5x(2 + -4x) Reorder the terms: -7 + 3x = 5x(2 + -4x) -7 + 3x = (2 * 5x + -4x * 5x) -7 + 3x = (10x + -20x2) Solving -7 + 3x = 10x + -20x2 Solving for variable 'x'. Combine like terms: 3x + -10x = -7x -7 + -7x + 20x2 = 10x + -20x2 + -10x + 20x2 Reorder the terms: -7 + -7x + 20x2 = 10x + -10x + -20x2 + 20x2 Combine like terms: 10x + -10x = 0 -7 + -7x + 20x2 = 0 + -20x2 + 20x2 -7 + -7x + 20x2 = -20x2 + 20x2 Combine like terms: -20x2 + 20x2 = 0 -7 + -7x + 20x2 = 0 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 = 0.791948134 x = 0.791948134 Simplifying x = 0.791948134Subproblem 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 = -0.441948134 x = -0.441948134 Simplifying x = -0.441948134Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.791948134, -0.441948134}
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