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Simplifying (6x + 4) + -1(x2 + x + -5) = 0 Reorder the terms: (4 + 6x) + -1(x2 + x + -5) = 0 Remove parenthesis around (4 + 6x) 4 + 6x + -1(x2 + x + -5) = 0 Reorder the terms: 4 + 6x + -1(-5 + x + x2) = 0 4 + 6x + (-5 * -1 + x * -1 + x2 * -1) = 0 4 + 6x + (5 + -1x + -1x2) = 0 Reorder the terms: 4 + 5 + 6x + -1x + -1x2 = 0 Combine like terms: 4 + 5 = 9 9 + 6x + -1x + -1x2 = 0 Combine like terms: 6x + -1x = 5x 9 + 5x + -1x2 = 0 Solving 9 + 5x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + -5x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -5x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -5x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5x + x2 = 0 + 9 -5x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -5x + x2 = 9 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 9 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 9 + 6.25 Combine like terms: 9 + 6.25 = 15.25 6.25 + -5x + x2 = 15.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + -2.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + -2.5 = 3.905124838 Simplifying x + -2.5 = 3.905124838 Reorder the terms: -2.5 + x = 3.905124838 Solving -2.5 + x = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.905124838 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.905124838 + 2.5 x = 3.905124838 + 2.5 Combine like terms: 3.905124838 + 2.5 = 6.405124838 x = 6.405124838 Simplifying x = 6.405124838Subproblem 2
x + -2.5 = -3.905124838 Simplifying x + -2.5 = -3.905124838 Reorder the terms: -2.5 + x = -3.905124838 Solving -2.5 + x = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.905124838 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.905124838 + 2.5 x = -3.905124838 + 2.5 Combine like terms: -3.905124838 + 2.5 = -1.405124838 x = -1.405124838 Simplifying x = -1.405124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.405124838, -1.405124838}
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