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Simplifying x(x + -5) = x(2) + 4x + 7 Reorder the terms: x(-5 + x) = x(2) + 4x + 7 (-5 * x + x * x) = x(2) + 4x + 7 (-5x + x2) = x(2) + 4x + 7 Reorder the terms for easier multiplication: -5x + x2 = 2x + 4x + 7 Reorder the terms: -5x + x2 = 7 + 2x + 4x Combine like terms: 2x + 4x = 6x -5x + x2 = 7 + 6x Solving -5x + x2 = 7 + 6x Solving for variable 'x'. Reorder the terms: -7 + -5x + -6x + x2 = 7 + 6x + -7 + -6x Combine like terms: -5x + -6x = -11x -7 + -11x + x2 = 7 + 6x + -7 + -6x Reorder the terms: -7 + -11x + x2 = 7 + -7 + 6x + -6x Combine like terms: 7 + -7 = 0 -7 + -11x + x2 = 0 + 6x + -6x -7 + -11x + x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -7 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -11x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -11x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -11x + x2 = 0 + 7 -11x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -11x + x2 = 7 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 7 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 7 + 30.25 Combine like terms: 7 + 30.25 = 37.25 30.25 + -11x + x2 = 37.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (x + -5.5) equal to 6.103277808 and -6.103277808.Subproblem 1
x + -5.5 = 6.103277808 Simplifying x + -5.5 = 6.103277808 Reorder the terms: -5.5 + x = 6.103277808 Solving -5.5 + x = 6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 6.103277808 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.103277808 + 5.5 x = 6.103277808 + 5.5 Combine like terms: 6.103277808 + 5.5 = 11.603277808 x = 11.603277808 Simplifying x = 11.603277808Subproblem 2
x + -5.5 = -6.103277808 Simplifying x + -5.5 = -6.103277808 Reorder the terms: -5.5 + x = -6.103277808 Solving -5.5 + x = -6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -6.103277808 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.103277808 + 5.5 x = -6.103277808 + 5.5 Combine like terms: -6.103277808 + 5.5 = -0.603277808 x = -0.603277808 Simplifying x = -0.603277808Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.603277808, -0.603277808}
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