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Simplifying -4x2 + -14x + 3 = 0 Reorder the terms: 3 + -14x + -4x2 = 0 Solving 3 + -14x + -4x2 = 0 Solving for variable 'x'. 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 = 0.202562419 x = 0.202562419 Simplifying x = 0.202562419Subproblem 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 = -3.702562419 x = -3.702562419 Simplifying x = -3.702562419Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.202562419, -3.702562419}
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