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Simplifying 32x2 + -3x + -14 = 0 Reorder the terms: -14 + -3x + 32x2 = 0 Solving -14 + -3x + 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'. -0.4375 + -0.09375x + x2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -0.09375x + 0.4375 + x2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -0.09375x + x2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -0.09375x + x2 = 0 + 0.4375 -0.09375x + x2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -0.09375x + x2 = 0.4375 The x term is -0.09375x. Take half its coefficient (-0.046875). Square it (0.002197265625) and add it to both sides. Add '0.002197265625' to each side of the equation. -0.09375x + 0.002197265625 + x2 = 0.4375 + 0.002197265625 Reorder the terms: 0.002197265625 + -0.09375x + x2 = 0.4375 + 0.002197265625 Combine like terms: 0.4375 + 0.002197265625 = 0.439697265625 0.002197265625 + -0.09375x + x2 = 0.439697265625 Factor a perfect square on the left side: (x + -0.046875)(x + -0.046875) = 0.439697265625 Calculate the square root of the right side: 0.663096724 Break this problem into two subproblems by setting (x + -0.046875) equal to 0.663096724 and -0.663096724.Subproblem 1
x + -0.046875 = 0.663096724 Simplifying x + -0.046875 = 0.663096724 Reorder the terms: -0.046875 + x = 0.663096724 Solving -0.046875 + x = 0.663096724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.046875' to each side of the equation. -0.046875 + 0.046875 + x = 0.663096724 + 0.046875 Combine like terms: -0.046875 + 0.046875 = 0.000000 0.000000 + x = 0.663096724 + 0.046875 x = 0.663096724 + 0.046875 Combine like terms: 0.663096724 + 0.046875 = 0.709971724 x = 0.709971724 Simplifying x = 0.709971724Subproblem 2
x + -0.046875 = -0.663096724 Simplifying x + -0.046875 = -0.663096724 Reorder the terms: -0.046875 + x = -0.663096724 Solving -0.046875 + x = -0.663096724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.046875' to each side of the equation. -0.046875 + 0.046875 + x = -0.663096724 + 0.046875 Combine like terms: -0.046875 + 0.046875 = 0.000000 0.000000 + x = -0.663096724 + 0.046875 x = -0.663096724 + 0.046875 Combine like terms: -0.663096724 + 0.046875 = -0.616221724 x = -0.616221724 Simplifying x = -0.616221724Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.709971724, -0.616221724}
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