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Simplifying -5x + -5x(x + -5) = -1(-5x + -1x) + -4 Reorder the terms: -5x + -5x(-5 + x) = -1(-5x + -1x) + -4 -5x + (-5 * -5x + x * -5x) = -1(-5x + -1x) + -4 -5x + (25x + -5x2) = -1(-5x + -1x) + -4 Combine like terms: -5x + 25x = 20x 20x + -5x2 = -1(-5x + -1x) + -4 Combine like terms: -5x + -1x = -6x 20x + -5x2 = -1(-6x) + -4 Remove parenthesis around (-6x) 20x + -5x2 = -1 * -6x + -4 Multiply -1 * -6 20x + -5x2 = 6x + -4 Reorder the terms: 20x + -5x2 = -4 + 6x Solving 20x + -5x2 = -4 + 6x Solving for variable 'x'. Reorder the terms: 4 + 20x + -6x + -5x2 = -4 + 6x + 4 + -6x Combine like terms: 20x + -6x = 14x 4 + 14x + -5x2 = -4 + 6x + 4 + -6x Reorder the terms: 4 + 14x + -5x2 = -4 + 4 + 6x + -6x Combine like terms: -4 + 4 = 0 4 + 14x + -5x2 = 0 + 6x + -6x 4 + 14x + -5x2 = 6x + -6x Combine like terms: 6x + -6x = 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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