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Simplifying 14x + -4x2 = 3.0625 Solving 14x + -4x2 = 3.0625 Solving for variable 'x'. Reorder the terms: -3.0625 + 14x + -4x2 = 3.0625 + -3.0625 Combine like terms: 3.0625 + -3.0625 = 0.0000 -3.0625 + 14x + -4x2 = 0.0000 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.765625 + -3.5x + x2 = 0.0000 Move the constant term to the right: Add '-0.765625' to each side of the equation. 0.765625 + -3.5x + -0.765625 + x2 = 0.0000 + -0.765625 Reorder the terms: 0.765625 + -0.765625 + -3.5x + x2 = 0.0000 + -0.765625 Combine like terms: 0.765625 + -0.765625 = 0.000000 0.000000 + -3.5x + x2 = 0.0000 + -0.765625 -3.5x + x2 = 0.0000 + -0.765625 Combine like terms: 0.0000 + -0.765625 = -0.765625 -3.5x + x2 = -0.765625 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -0.765625 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -0.765625 + 3.0625 Combine like terms: -0.765625 + 3.0625 = 2.296875 3.0625 + -3.5x + x2 = 2.296875 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 2.296875 Calculate the square root of the right side: 1.515544457 Break this problem into two subproblems by setting (x + -1.75) equal to 1.515544457 and -1.515544457.Subproblem 1
x + -1.75 = 1.515544457 Simplifying x + -1.75 = 1.515544457 Reorder the terms: -1.75 + x = 1.515544457 Solving -1.75 + x = 1.515544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.515544457 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.515544457 + 1.75 x = 1.515544457 + 1.75 Combine like terms: 1.515544457 + 1.75 = 3.265544457 x = 3.265544457 Simplifying x = 3.265544457Subproblem 2
x + -1.75 = -1.515544457 Simplifying x + -1.75 = -1.515544457 Reorder the terms: -1.75 + x = -1.515544457 Solving -1.75 + x = -1.515544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.515544457 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.515544457 + 1.75 x = -1.515544457 + 1.75 Combine like terms: -1.515544457 + 1.75 = 0.234455543 x = 0.234455543 Simplifying x = 0.234455543Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.265544457, 0.234455543}
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