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Simplifying 4x2 + -14x = 3 Reorder the terms: -14x + 4x2 = 3 Solving -14x + 4x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + -14x + 4x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -14x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + -3.5x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -3.5x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -3.5x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -3.5x + x2 = 0 + 0.75 -3.5x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -3.5x + x2 = 0.75 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 = 0.75 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 0.75 + 3.0625 Combine like terms: 0.75 + 3.0625 = 3.8125 3.0625 + -3.5x + x2 = 3.8125 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 3.8125 Calculate the square root of the right side: 1.952562419 Break this problem into two subproblems by setting (x + -1.75) equal to 1.952562419 and -1.952562419.Subproblem 1
x + -1.75 = 1.952562419 Simplifying x + -1.75 = 1.952562419 Reorder the terms: -1.75 + x = 1.952562419 Solving -1.75 + x = 1.952562419 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 = 1.952562419 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.952562419 + 1.75 x = 1.952562419 + 1.75 Combine like terms: 1.952562419 + 1.75 = 3.702562419 x = 3.702562419 Simplifying x = 3.702562419Subproblem 2
x + -1.75 = -1.952562419 Simplifying x + -1.75 = -1.952562419 Reorder the terms: -1.75 + x = -1.952562419 Solving -1.75 + x = -1.952562419 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 = -1.952562419 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.952562419 + 1.75 x = -1.952562419 + 1.75 Combine like terms: -1.952562419 + 1.75 = -0.202562419 x = -0.202562419 Simplifying x = -0.202562419Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.702562419, -0.202562419}
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