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Simplifying 5 = (x + -4)(x + 3) Reorder the terms: 5 = (-4 + x)(x + 3) Reorder the terms: 5 = (-4 + x)(3 + x) Multiply (-4 + x) * (3 + x) 5 = (-4(3 + x) + x(3 + x)) 5 = ((3 * -4 + x * -4) + x(3 + x)) 5 = ((-12 + -4x) + x(3 + x)) 5 = (-12 + -4x + (3 * x + x * x)) 5 = (-12 + -4x + (3x + x2)) Combine like terms: -4x + 3x = -1x 5 = (-12 + -1x + x2) Solving 5 = -12 + -1x + x2 Solving for variable 'x'. Combine like terms: 5 + 12 = 17 17 + x + -1x2 = -12 + -1x + x2 + 12 + x + -1x2 Reorder the terms: 17 + x + -1x2 = -12 + 12 + -1x + x + x2 + -1x2 Combine like terms: -12 + 12 = 0 17 + x + -1x2 = 0 + -1x + x + x2 + -1x2 17 + x + -1x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 17 + x + -1x2 = 0 + x2 + -1x2 17 + x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 17 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -17 + -1x + x2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + -1x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -1x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -1x + x2 = 0 + 17 -1x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -1x + x2 = 17 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. -1x + 0.25 + x2 = 17 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 17 + 0.25 Combine like terms: 17 + 0.25 = 17.25 0.25 + -1x + x2 = 17.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (x + 0.5) equal to 4.153311931 and -4.153311931.Subproblem 1
x + 0.5 = 4.153311931 Simplifying x + 0.5 = 4.153311931 Reorder the terms: 0.5 + x = 4.153311931 Solving 0.5 + x = 4.153311931 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 = 4.153311931 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.153311931 + -0.5 x = 4.153311931 + -0.5 Combine like terms: 4.153311931 + -0.5 = 3.653311931 x = 3.653311931 Simplifying x = 3.653311931Subproblem 2
x + 0.5 = -4.153311931 Simplifying x + 0.5 = -4.153311931 Reorder the terms: 0.5 + x = -4.153311931 Solving 0.5 + x = -4.153311931 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 = -4.153311931 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.153311931 + -0.5 x = -4.153311931 + -0.5 Combine like terms: -4.153311931 + -0.5 = -4.653311931 x = -4.653311931 Simplifying x = -4.653311931Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.653311931, -4.653311931}
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