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Simplifying (x + 4)(x + -3) = 3 Reorder the terms: (4 + x)(x + -3) = 3 Reorder the terms: (4 + x)(-3 + x) = 3 Multiply (4 + x) * (-3 + x) (4(-3 + x) + x(-3 + x)) = 3 ((-3 * 4 + x * 4) + x(-3 + x)) = 3 ((-12 + 4x) + x(-3 + x)) = 3 (-12 + 4x + (-3 * x + x * x)) = 3 (-12 + 4x + (-3x + x2)) = 3 Combine like terms: 4x + -3x = 1x (-12 + 1x + x2) = 3 Solving -12 + 1x + x2 = 3 Solving for variable 'x'. Reorder the terms: -12 + -3 + 1x + x2 = 3 + -3 Combine like terms: -12 + -3 = -15 -15 + 1x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -15 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 1x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 1x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 1x + x2 = 0 + 15 1x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 1x + x2 = 15 The x term is 1x. 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. x + 0.25 + x2 = 15 + 0.25 Reorder the terms: 0.25 + x + x2 = 15 + 0.25 Combine like terms: 15 + 0.25 = 15.25 0.25 + x + 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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