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Simplifying x(x + -10) = (x + -5)(2x + 7) Reorder the terms: x(-10 + x) = (x + -5)(2x + 7) (-10 * x + x * x) = (x + -5)(2x + 7) (-10x + x2) = (x + -5)(2x + 7) Reorder the terms: -10x + x2 = (-5 + x)(2x + 7) Reorder the terms: -10x + x2 = (-5 + x)(7 + 2x) Multiply (-5 + x) * (7 + 2x) -10x + x2 = (-5(7 + 2x) + x(7 + 2x)) -10x + x2 = ((7 * -5 + 2x * -5) + x(7 + 2x)) -10x + x2 = ((-35 + -10x) + x(7 + 2x)) -10x + x2 = (-35 + -10x + (7 * x + 2x * x)) -10x + x2 = (-35 + -10x + (7x + 2x2)) Combine like terms: -10x + 7x = -3x -10x + x2 = (-35 + -3x + 2x2) Solving -10x + x2 = -35 + -3x + 2x2 Solving for variable 'x'. Reorder the terms: 35 + -10x + 3x + x2 + -2x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2 Combine like terms: -10x + 3x = -7x 35 + -7x + x2 + -2x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2 Combine like terms: x2 + -2x2 = -1x2 35 + -7x + -1x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2 Reorder the terms: 35 + -7x + -1x2 = -35 + 35 + -3x + 3x + 2x2 + -2x2 Combine like terms: -35 + 35 = 0 35 + -7x + -1x2 = 0 + -3x + 3x + 2x2 + -2x2 35 + -7x + -1x2 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 0 35 + -7x + -1x2 = 0 + 2x2 + -2x2 35 + -7x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 35 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -35 + 7x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + 7x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + 7x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 7x + x2 = 0 + 35 7x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 7x + x2 = 35 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 35 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 35 + 12.25 Combine like terms: 35 + 12.25 = 47.25 12.25 + 7x + x2 = 47.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (x + 3.5) equal to 6.873863542 and -6.873863542.Subproblem 1
x + 3.5 = 6.873863542 Simplifying x + 3.5 = 6.873863542 Reorder the terms: 3.5 + x = 6.873863542 Solving 3.5 + x = 6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 6.873863542 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.873863542 + -3.5 x = 6.873863542 + -3.5 Combine like terms: 6.873863542 + -3.5 = 3.373863542 x = 3.373863542 Simplifying x = 3.373863542Subproblem 2
x + 3.5 = -6.873863542 Simplifying x + 3.5 = -6.873863542 Reorder the terms: 3.5 + x = -6.873863542 Solving 3.5 + x = -6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -6.873863542 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.873863542 + -3.5 x = -6.873863542 + -3.5 Combine like terms: -6.873863542 + -3.5 = -10.373863542 x = -10.373863542 Simplifying x = -10.373863542Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.373863542, -10.373863542}
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