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Simplifying x(x + -3) = x(2) + 5x + 7 Reorder the terms: x(-3 + x) = x(2) + 5x + 7 (-3 * x + x * x) = x(2) + 5x + 7 (-3x + x2) = x(2) + 5x + 7 Reorder the terms for easier multiplication: -3x + x2 = 2x + 5x + 7 Reorder the terms: -3x + x2 = 7 + 2x + 5x Combine like terms: 2x + 5x = 7x -3x + x2 = 7 + 7x Solving -3x + x2 = 7 + 7x Solving for variable 'x'. Reorder the terms: -7 + -3x + -7x + x2 = 7 + 7x + -7 + -7x Combine like terms: -3x + -7x = -10x -7 + -10x + x2 = 7 + 7x + -7 + -7x Reorder the terms: -7 + -10x + x2 = 7 + -7 + 7x + -7x Combine like terms: 7 + -7 = 0 -7 + -10x + x2 = 0 + 7x + -7x -7 + -10x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -7 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -10x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -10x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -10x + x2 = 0 + 7 -10x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -10x + x2 = 7 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 7 + 25 Reorder the terms: 25 + -10x + x2 = 7 + 25 Combine like terms: 7 + 25 = 32 25 + -10x + x2 = 32 Factor a perfect square on the left side: (x + -5)(x + -5) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + -5) equal to 5.656854249 and -5.656854249.Subproblem 1
x + -5 = 5.656854249 Simplifying x + -5 = 5.656854249 Reorder the terms: -5 + x = 5.656854249 Solving -5 + x = 5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.656854249 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.656854249 + 5 x = 5.656854249 + 5 Combine like terms: 5.656854249 + 5 = 10.656854249 x = 10.656854249 Simplifying x = 10.656854249Subproblem 2
x + -5 = -5.656854249 Simplifying x + -5 = -5.656854249 Reorder the terms: -5 + x = -5.656854249 Solving -5 + x = -5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.656854249 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.656854249 + 5 x = -5.656854249 + 5 Combine like terms: -5.656854249 + 5 = -0.656854249 x = -0.656854249 Simplifying x = -0.656854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.656854249, -0.656854249}
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