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Simplifying 20x2 + 7x + -12 = 0 Reorder the terms: -12 + 7x + 20x2 = 0 Solving -12 + 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'. -0.6 + 0.35x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 0.35x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 0.35x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 0.35x + x2 = 0 + 0.6 0.35x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 0.35x + x2 = 0.6 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 = 0.6 + 0.030625 Reorder the terms: 0.030625 + 0.35x + x2 = 0.6 + 0.030625 Combine like terms: 0.6 + 0.030625 = 0.630625 0.030625 + 0.35x + x2 = 0.630625 Factor a perfect square on the left side: (x + 0.175)(x + 0.175) = 0.630625 Calculate the square root of the right side: 0.794119009 Break this problem into two subproblems by setting (x + 0.175) equal to 0.794119009 and -0.794119009.Subproblem 1
x + 0.175 = 0.794119009 Simplifying x + 0.175 = 0.794119009 Reorder the terms: 0.175 + x = 0.794119009 Solving 0.175 + x = 0.794119009 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 = 0.794119009 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + x = 0.794119009 + -0.175 x = 0.794119009 + -0.175 Combine like terms: 0.794119009 + -0.175 = 0.619119009 x = 0.619119009 Simplifying x = 0.619119009Subproblem 2
x + 0.175 = -0.794119009 Simplifying x + 0.175 = -0.794119009 Reorder the terms: 0.175 + x = -0.794119009 Solving 0.175 + x = -0.794119009 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 = -0.794119009 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + x = -0.794119009 + -0.175 x = -0.794119009 + -0.175 Combine like terms: -0.794119009 + -0.175 = -0.969119009 x = -0.969119009 Simplifying x = -0.969119009Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.619119009, -0.969119009}
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