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Simplifying (x + 2)(x + -3) + 2 = 7(2x + 4) + -19 Reorder the terms: (2 + x)(x + -3) + 2 = 7(2x + 4) + -19 Reorder the terms: (2 + x)(-3 + x) + 2 = 7(2x + 4) + -19 Multiply (2 + x) * (-3 + x) (2(-3 + x) + x(-3 + x)) + 2 = 7(2x + 4) + -19 ((-3 * 2 + x * 2) + x(-3 + x)) + 2 = 7(2x + 4) + -19 ((-6 + 2x) + x(-3 + x)) + 2 = 7(2x + 4) + -19 (-6 + 2x + (-3 * x + x * x)) + 2 = 7(2x + 4) + -19 (-6 + 2x + (-3x + x2)) + 2 = 7(2x + 4) + -19 Combine like terms: 2x + -3x = -1x (-6 + -1x + x2) + 2 = 7(2x + 4) + -19 Reorder the terms: -6 + 2 + -1x + x2 = 7(2x + 4) + -19 Combine like terms: -6 + 2 = -4 -4 + -1x + x2 = 7(2x + 4) + -19 Reorder the terms: -4 + -1x + x2 = 7(4 + 2x) + -19 -4 + -1x + x2 = (4 * 7 + 2x * 7) + -19 -4 + -1x + x2 = (28 + 14x) + -19 Reorder the terms: -4 + -1x + x2 = 28 + -19 + 14x Combine like terms: 28 + -19 = 9 -4 + -1x + x2 = 9 + 14x Solving -4 + -1x + x2 = 9 + 14x Solving for variable 'x'. Reorder the terms: -4 + -9 + -1x + -14x + x2 = 9 + 14x + -9 + -14x Combine like terms: -4 + -9 = -13 -13 + -1x + -14x + x2 = 9 + 14x + -9 + -14x Combine like terms: -1x + -14x = -15x -13 + -15x + x2 = 9 + 14x + -9 + -14x Reorder the terms: -13 + -15x + x2 = 9 + -9 + 14x + -14x Combine like terms: 9 + -9 = 0 -13 + -15x + x2 = 0 + 14x + -14x -13 + -15x + x2 = 14x + -14x Combine like terms: 14x + -14x = 0 -13 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -15x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -15x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -15x + x2 = 0 + 13 -15x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -15x + x2 = 13 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 13 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 13 + 56.25 Combine like terms: 13 + 56.25 = 69.25 56.25 + -15x + x2 = 69.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 69.25 Calculate the square root of the right side: 8.321658489 Break this problem into two subproblems by setting (x + -7.5) equal to 8.321658489 and -8.321658489.Subproblem 1
x + -7.5 = 8.321658489 Simplifying x + -7.5 = 8.321658489 Reorder the terms: -7.5 + x = 8.321658489 Solving -7.5 + x = 8.321658489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 8.321658489 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 8.321658489 + 7.5 x = 8.321658489 + 7.5 Combine like terms: 8.321658489 + 7.5 = 15.821658489 x = 15.821658489 Simplifying x = 15.821658489Subproblem 2
x + -7.5 = -8.321658489 Simplifying x + -7.5 = -8.321658489 Reorder the terms: -7.5 + x = -8.321658489 Solving -7.5 + x = -8.321658489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -8.321658489 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -8.321658489 + 7.5 x = -8.321658489 + 7.5 Combine like terms: -8.321658489 + 7.5 = -0.821658489 x = -0.821658489 Simplifying x = -0.821658489Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.821658489, -0.821658489}
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