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Simplifying (x + 3)(x + -4) = 1445 Reorder the terms: (3 + x)(x + -4) = 1445 Reorder the terms: (3 + x)(-4 + x) = 1445 Multiply (3 + x) * (-4 + x) (3(-4 + x) + x(-4 + x)) = 1445 ((-4 * 3 + x * 3) + x(-4 + x)) = 1445 ((-12 + 3x) + x(-4 + x)) = 1445 (-12 + 3x + (-4 * x + x * x)) = 1445 (-12 + 3x + (-4x + x2)) = 1445 Combine like terms: 3x + -4x = -1x (-12 + -1x + x2) = 1445 Solving -12 + -1x + x2 = 1445 Solving for variable 'x'. Reorder the terms: -12 + -1445 + -1x + x2 = 1445 + -1445 Combine like terms: -12 + -1445 = -1457 -1457 + -1x + x2 = 1445 + -1445 Combine like terms: 1445 + -1445 = 0 -1457 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1457' to each side of the equation. -1457 + -1x + 1457 + x2 = 0 + 1457 Reorder the terms: -1457 + 1457 + -1x + x2 = 0 + 1457 Combine like terms: -1457 + 1457 = 0 0 + -1x + x2 = 0 + 1457 -1x + x2 = 0 + 1457 Combine like terms: 0 + 1457 = 1457 -1x + x2 = 1457 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. -1x + 0.25 + x2 = 1457 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1457 + 0.25 Combine like terms: 1457 + 0.25 = 1457.25 0.25 + -1x + x2 = 1457.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1457.25 Calculate the square root of the right side: 38.173943993 Break this problem into two subproblems by setting (x + -0.5) equal to 38.173943993 and -38.173943993.Subproblem 1
x + -0.5 = 38.173943993 Simplifying x + -0.5 = 38.173943993 Reorder the terms: -0.5 + x = 38.173943993 Solving -0.5 + x = 38.173943993 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 = 38.173943993 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 38.173943993 + 0.5 x = 38.173943993 + 0.5 Combine like terms: 38.173943993 + 0.5 = 38.673943993 x = 38.673943993 Simplifying x = 38.673943993Subproblem 2
x + -0.5 = -38.173943993 Simplifying x + -0.5 = -38.173943993 Reorder the terms: -0.5 + x = -38.173943993 Solving -0.5 + x = -38.173943993 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 = -38.173943993 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -38.173943993 + 0.5 x = -38.173943993 + 0.5 Combine like terms: -38.173943993 + 0.5 = -37.673943993 x = -37.673943993 Simplifying x = -37.673943993Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.673943993, -37.673943993}
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