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Simplifying 32x2 + -7x + -12 = 0 Reorder the terms: -12 + -7x + 32x2 = 0 Solving -12 + -7x + 32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.375 + -0.21875x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -0.21875x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -0.21875x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -0.21875x + x2 = 0 + 0.375 -0.21875x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -0.21875x + x2 = 0.375 The x term is -0.21875x. Take half its coefficient (-0.109375). Square it (0.01196289063) and add it to both sides. Add '0.01196289063' to each side of the equation. -0.21875x + 0.01196289063 + x2 = 0.375 + 0.01196289063 Reorder the terms: 0.01196289063 + -0.21875x + x2 = 0.375 + 0.01196289063 Combine like terms: 0.375 + 0.01196289063 = 0.38696289063 0.01196289063 + -0.21875x + x2 = 0.38696289063 Factor a perfect square on the left side: (x + -0.109375)(x + -0.109375) = 0.38696289063 Calculate the square root of the right side: 0.622063414 Break this problem into two subproblems by setting (x + -0.109375) equal to 0.622063414 and -0.622063414.Subproblem 1
x + -0.109375 = 0.622063414 Simplifying x + -0.109375 = 0.622063414 Reorder the terms: -0.109375 + x = 0.622063414 Solving -0.109375 + x = 0.622063414 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.109375' to each side of the equation. -0.109375 + 0.109375 + x = 0.622063414 + 0.109375 Combine like terms: -0.109375 + 0.109375 = 0.000000 0.000000 + x = 0.622063414 + 0.109375 x = 0.622063414 + 0.109375 Combine like terms: 0.622063414 + 0.109375 = 0.731438414 x = 0.731438414 Simplifying x = 0.731438414Subproblem 2
x + -0.109375 = -0.622063414 Simplifying x + -0.109375 = -0.622063414 Reorder the terms: -0.109375 + x = -0.622063414 Solving -0.109375 + x = -0.622063414 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.109375' to each side of the equation. -0.109375 + 0.109375 + x = -0.622063414 + 0.109375 Combine like terms: -0.109375 + 0.109375 = 0.000000 0.000000 + x = -0.622063414 + 0.109375 x = -0.622063414 + 0.109375 Combine like terms: -0.622063414 + 0.109375 = -0.512688414 x = -0.512688414 Simplifying x = -0.512688414Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.731438414, -0.512688414}
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