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Simplifying x = (x + -3)(x + 5) Reorder the terms: x = (-3 + x)(x + 5) Reorder the terms: x = (-3 + x)(5 + x) Multiply (-3 + x) * (5 + x) x = (-3(5 + x) + x(5 + x)) x = ((5 * -3 + x * -3) + x(5 + x)) x = ((-15 + -3x) + x(5 + x)) x = (-15 + -3x + (5 * x + x * x)) x = (-15 + -3x + (5x + x2)) Combine like terms: -3x + 5x = 2x x = (-15 + 2x + x2) Solving x = -15 + 2x + x2 Solving for variable 'x'. Reorder the terms: 15 + x + -2x + -1x2 = -15 + 2x + x2 + 15 + -2x + -1x2 Combine like terms: x + -2x = -1x 15 + -1x + -1x2 = -15 + 2x + x2 + 15 + -2x + -1x2 Reorder the terms: 15 + -1x + -1x2 = -15 + 15 + 2x + -2x + x2 + -1x2 Combine like terms: -15 + 15 = 0 15 + -1x + -1x2 = 0 + 2x + -2x + x2 + -1x2 15 + -1x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 15 + -1x + -1x2 = 0 + x2 + -1x2 15 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 15 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + x + x2 = 0 + 15 x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 x + x2 = 15 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 15 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 15 + 0.25 Combine like terms: 15 + 0.25 = 15.25 1.25 + x2 = 15.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + 0.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + 0.5 = 3.905124838 Simplifying x + 0.5 = 3.905124838 Reorder the terms: 0.5 + x = 3.905124838 Solving 0.5 + x = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.905124838 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.905124838 + -0.5 x = 3.905124838 + -0.5 Combine like terms: 3.905124838 + -0.5 = 3.405124838 x = 3.405124838 Simplifying x = 3.405124838Subproblem 2
x + 0.5 = -3.905124838 Simplifying x + 0.5 = -3.905124838 Reorder the terms: 0.5 + x = -3.905124838 Solving 0.5 + x = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.905124838 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.905124838 + -0.5 x = -3.905124838 + -0.5 Combine like terms: -3.905124838 + -0.5 = -4.405124838 x = -4.405124838 Simplifying x = -4.405124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.405124838, -4.405124838}
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