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Simplifying -2x2 + 0.7x + 0.3 = 0 Reorder the terms: 0.3 + 0.7x + -2x2 = 0 Solving 0.3 + 0.7x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.15 + -0.35x + x2 = 0 Move the constant term to the right: Add '0.15' to each side of the equation. -0.15 + -0.35x + 0.15 + x2 = 0 + 0.15 Reorder the terms: -0.15 + 0.15 + -0.35x + x2 = 0 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + -0.35x + x2 = 0 + 0.15 -0.35x + x2 = 0 + 0.15 Combine like terms: 0 + 0.15 = 0.15 -0.35x + x2 = 0.15 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 = 0.15 + 0.030625 Reorder the terms: 0.030625 + -0.35x + x2 = 0.15 + 0.030625 Combine like terms: 0.15 + 0.030625 = 0.180625 0.030625 + -0.35x + x2 = 0.180625 Factor a perfect square on the left side: (x + -0.175)(x + -0.175) = 0.180625 Calculate the square root of the right side: 0.425 Break this problem into two subproblems by setting (x + -0.175) equal to 0.425 and -0.425.Subproblem 1
x + -0.175 = 0.425 Simplifying x + -0.175 = 0.425 Reorder the terms: -0.175 + x = 0.425 Solving -0.175 + x = 0.425 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 = 0.425 + 0.175 Combine like terms: -0.175 + 0.175 = 0.000 0.000 + x = 0.425 + 0.175 x = 0.425 + 0.175 Combine like terms: 0.425 + 0.175 = 0.6 x = 0.6 Simplifying x = 0.6Subproblem 2
x + -0.175 = -0.425 Simplifying x + -0.175 = -0.425 Reorder the terms: -0.175 + x = -0.425 Solving -0.175 + x = -0.425 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 = -0.425 + 0.175 Combine like terms: -0.175 + 0.175 = 0.000 0.000 + x = -0.425 + 0.175 x = -0.425 + 0.175 Combine like terms: -0.425 + 0.175 = -0.25 x = -0.25 Simplifying x = -0.25Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6, -0.25}
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