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Simplifying x(x + 2) + -72 = 3x + 6 Reorder the terms: x(2 + x) + -72 = 3x + 6 (2 * x + x * x) + -72 = 3x + 6 (2x + x2) + -72 = 3x + 6 Reorder the terms: -72 + 2x + x2 = 3x + 6 Reorder the terms: -72 + 2x + x2 = 6 + 3x Solving -72 + 2x + x2 = 6 + 3x Solving for variable 'x'. Reorder the terms: -72 + -6 + 2x + -3x + x2 = 6 + 3x + -6 + -3x Combine like terms: -72 + -6 = -78 -78 + 2x + -3x + x2 = 6 + 3x + -6 + -3x Combine like terms: 2x + -3x = -1x -78 + -1x + x2 = 6 + 3x + -6 + -3x Reorder the terms: -78 + -1x + x2 = 6 + -6 + 3x + -3x Combine like terms: 6 + -6 = 0 -78 + -1x + x2 = 0 + 3x + -3x -78 + -1x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -78 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '78' to each side of the equation. -78 + -1x + 78 + x2 = 0 + 78 Reorder the terms: -78 + 78 + -1x + x2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + -1x + x2 = 0 + 78 -1x + x2 = 0 + 78 Combine like terms: 0 + 78 = 78 -1x + x2 = 78 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 = 78 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 78 + 0.25 Combine like terms: 78 + 0.25 = 78.25 0.25 + -1x + x2 = 78.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (x + -0.5) equal to 8.845903006 and -8.845903006.Subproblem 1
x + -0.5 = 8.845903006 Simplifying x + -0.5 = 8.845903006 Reorder the terms: -0.5 + x = 8.845903006 Solving -0.5 + x = 8.845903006 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 = 8.845903006 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 8.845903006 + 0.5 x = 8.845903006 + 0.5 Combine like terms: 8.845903006 + 0.5 = 9.345903006 x = 9.345903006 Simplifying x = 9.345903006Subproblem 2
x + -0.5 = -8.845903006 Simplifying x + -0.5 = -8.845903006 Reorder the terms: -0.5 + x = -8.845903006 Solving -0.5 + x = -8.845903006 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 = -8.845903006 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -8.845903006 + 0.5 x = -8.845903006 + 0.5 Combine like terms: -8.845903006 + 0.5 = -8.345903006 x = -8.345903006 Simplifying x = -8.345903006Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.345903006, -8.345903006}
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