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Simplifying x(4 + -1x) + -1(5 + -1x)(x + -5) = x(x + 1) (4 * x + -1x * x) + -1(5 + -1x)(x + -5) = x(x + 1) (4x + -1x2) + -1(5 + -1x)(x + -5) = x(x + 1) Reorder the terms: 4x + -1x2 + -1(5 + -1x)(-5 + x) = x(x + 1) Multiply (5 + -1x) * (-5 + x) 4x + -1x2 + -1(5(-5 + x) + -1x * (-5 + x)) = x(x + 1) 4x + -1x2 + -1((-5 * 5 + x * 5) + -1x * (-5 + x)) = x(x + 1) 4x + -1x2 + -1((-25 + 5x) + -1x * (-5 + x)) = x(x + 1) 4x + -1x2 + -1(-25 + 5x + (-5 * -1x + x * -1x)) = x(x + 1) 4x + -1x2 + -1(-25 + 5x + (5x + -1x2)) = x(x + 1) Combine like terms: 5x + 5x = 10x 4x + -1x2 + -1(-25 + 10x + -1x2) = x(x + 1) 4x + -1x2 + (-25 * -1 + 10x * -1 + -1x2 * -1) = x(x + 1) 4x + -1x2 + (25 + -10x + 1x2) = x(x + 1) Reorder the terms: 25 + 4x + -10x + -1x2 + 1x2 = x(x + 1) Combine like terms: 4x + -10x = -6x 25 + -6x + -1x2 + 1x2 = x(x + 1) Combine like terms: -1x2 + 1x2 = 0 25 + -6x + 0 = x(x + 1) 25 + -6x = x(x + 1) Reorder the terms: 25 + -6x = x(1 + x) 25 + -6x = (1 * x + x * x) 25 + -6x = (1x + x2) Solving 25 + -6x = 1x + x2 Solving for variable 'x'. Combine like terms: -6x + -1x = -7x 25 + -7x + -1x2 = 1x + x2 + -1x + -1x2 Reorder the terms: 25 + -7x + -1x2 = 1x + -1x + x2 + -1x2 Combine like terms: 1x + -1x = 0 25 + -7x + -1x2 = 0 + x2 + -1x2 25 + -7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 25 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + 7x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 7x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 7x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 7x + x2 = 0 + 25 7x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 7x + x2 = 25 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 25 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 25 + 12.25 Combine like terms: 25 + 12.25 = 37.25 12.25 + 7x + x2 = 37.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (x + 3.5) equal to 6.103277808 and -6.103277808.Subproblem 1
x + 3.5 = 6.103277808 Simplifying x + 3.5 = 6.103277808 Reorder the terms: 3.5 + x = 6.103277808 Solving 3.5 + x = 6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 6.103277808 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.103277808 + -3.5 x = 6.103277808 + -3.5 Combine like terms: 6.103277808 + -3.5 = 2.603277808 x = 2.603277808 Simplifying x = 2.603277808Subproblem 2
x + 3.5 = -6.103277808 Simplifying x + 3.5 = -6.103277808 Reorder the terms: 3.5 + x = -6.103277808 Solving 3.5 + x = -6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -6.103277808 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.103277808 + -3.5 x = -6.103277808 + -3.5 Combine like terms: -6.103277808 + -3.5 = -9.603277808 x = -9.603277808 Simplifying x = -9.603277808Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.603277808, -9.603277808}
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