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Simplifying (2x + -7)(x + 3) = 3 Reorder the terms: (-7 + 2x)(x + 3) = 3 Reorder the terms: (-7 + 2x)(3 + x) = 3 Multiply (-7 + 2x) * (3 + x) (-7(3 + x) + 2x * (3 + x)) = 3 ((3 * -7 + x * -7) + 2x * (3 + x)) = 3 ((-21 + -7x) + 2x * (3 + x)) = 3 (-21 + -7x + (3 * 2x + x * 2x)) = 3 (-21 + -7x + (6x + 2x2)) = 3 Combine like terms: -7x + 6x = -1x (-21 + -1x + 2x2) = 3 Solving -21 + -1x + 2x2 = 3 Solving for variable 'x'. Reorder the terms: -21 + -3 + -1x + 2x2 = 3 + -3 Combine like terms: -21 + -3 = -24 -24 + -1x + 2x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -24 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12 + -0.5x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -0.5x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -0.5x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -0.5x + x2 = 0 + 12 -0.5x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -0.5x + x2 = 12 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 12 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 12 + 0.0625 Combine like terms: 12 + 0.0625 = 12.0625 0.0625 + -0.5x + x2 = 12.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting (x + -0.25) equal to 3.473110997 and -3.473110997.Subproblem 1
x + -0.25 = 3.473110997 Simplifying x + -0.25 = 3.473110997 Reorder the terms: -0.25 + x = 3.473110997 Solving -0.25 + x = 3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 3.473110997 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 3.473110997 + 0.25 x = 3.473110997 + 0.25 Combine like terms: 3.473110997 + 0.25 = 3.723110997 x = 3.723110997 Simplifying x = 3.723110997Subproblem 2
x + -0.25 = -3.473110997 Simplifying x + -0.25 = -3.473110997 Reorder the terms: -0.25 + x = -3.473110997 Solving -0.25 + x = -3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -3.473110997 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -3.473110997 + 0.25 x = -3.473110997 + 0.25 Combine like terms: -3.473110997 + 0.25 = -3.223110997 x = -3.223110997 Simplifying x = -3.223110997Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.723110997, -3.223110997}
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