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Simplifying 5x2 = 14x + 4 Reorder the terms: 5x2 = 4 + 14x Solving 5x2 = 4 + 14x Solving for variable 'x'. Reorder the terms: -4 + -14x + 5x2 = 4 + 14x + -4 + -14x Reorder the terms: -4 + -14x + 5x2 = 4 + -4 + 14x + -14x Combine like terms: 4 + -4 = 0 -4 + -14x + 5x2 = 0 + 14x + -14x -4 + -14x + 5x2 = 14x + -14x Combine like terms: 14x + -14x = 0 -4 + -14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -2.8x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -2.8x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -2.8x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -2.8x + x2 = 0 + 0.8 -2.8x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -2.8x + x2 = 0.8 The x term is -2.8x. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8x + 1.96 + x2 = 0.8 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = 0.8 + 1.96 Combine like terms: 0.8 + 1.96 = 2.76 1.96 + -2.8x + x2 = 2.76 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 2.76 Calculate the square root of the right side: 1.661324773 Break this problem into two subproblems by setting (x + -1.4) equal to 1.661324773 and -1.661324773.Subproblem 1
x + -1.4 = 1.661324773 Simplifying x + -1.4 = 1.661324773 Reorder the terms: -1.4 + x = 1.661324773 Solving -1.4 + x = 1.661324773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 1.661324773 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 1.661324773 + 1.4 x = 1.661324773 + 1.4 Combine like terms: 1.661324773 + 1.4 = 3.061324773 x = 3.061324773 Simplifying x = 3.061324773Subproblem 2
x + -1.4 = -1.661324773 Simplifying x + -1.4 = -1.661324773 Reorder the terms: -1.4 + x = -1.661324773 Solving -1.4 + x = -1.661324773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -1.661324773 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -1.661324773 + 1.4 x = -1.661324773 + 1.4 Combine like terms: -1.661324773 + 1.4 = -0.261324773 x = -0.261324773 Simplifying x = -0.261324773Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.061324773, -0.261324773}
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