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Simplifying 5x(x + -1) + -1(5x + -2) = 0 Reorder the terms: 5x(-1 + x) + -1(5x + -2) = 0 (-1 * 5x + x * 5x) + -1(5x + -2) = 0 (-5x + 5x2) + -1(5x + -2) = 0 Reorder the terms: -5x + 5x2 + -1(-2 + 5x) = 0 -5x + 5x2 + (-2 * -1 + 5x * -1) = 0 -5x + 5x2 + (2 + -5x) = 0 Reorder the terms: 2 + -5x + -5x + 5x2 = 0 Combine like terms: -5x + -5x = -10x 2 + -10x + 5x2 = 0 Solving 2 + -10x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -2x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -2x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -2x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -2x + x2 = 0 + -0.4 -2x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -2x + x2 = -0.4 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.4 + 1 Reorder the terms: 1 + -2x + x2 = -0.4 + 1 Combine like terms: -0.4 + 1 = 0.6 1 + -2x + x2 = 0.6 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.6 Calculate the square root of the right side: 0.774596669 Break this problem into two subproblems by setting (x + -1) equal to 0.774596669 and -0.774596669.Subproblem 1
x + -1 = 0.774596669 Simplifying x + -1 = 0.774596669 Reorder the terms: -1 + x = 0.774596669 Solving -1 + x = 0.774596669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.774596669 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.774596669 + 1 x = 0.774596669 + 1 Combine like terms: 0.774596669 + 1 = 1.774596669 x = 1.774596669 Simplifying x = 1.774596669Subproblem 2
x + -1 = -0.774596669 Simplifying x + -1 = -0.774596669 Reorder the terms: -1 + x = -0.774596669 Solving -1 + x = -0.774596669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.774596669 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.774596669 + 1 x = -0.774596669 + 1 Combine like terms: -0.774596669 + 1 = 0.225403331 x = 0.225403331 Simplifying x = 0.225403331Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.774596669, 0.225403331}
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