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Simplifying (2x + -2)(2x + -2) + 5 = 10 Reorder the terms: (-2 + 2x)(2x + -2) + 5 = 10 Reorder the terms: (-2 + 2x)(-2 + 2x) + 5 = 10 Multiply (-2 + 2x) * (-2 + 2x) (-2(-2 + 2x) + 2x * (-2 + 2x)) + 5 = 10 ((-2 * -2 + 2x * -2) + 2x * (-2 + 2x)) + 5 = 10 ((4 + -4x) + 2x * (-2 + 2x)) + 5 = 10 (4 + -4x + (-2 * 2x + 2x * 2x)) + 5 = 10 (4 + -4x + (-4x + 4x2)) + 5 = 10 Combine like terms: -4x + -4x = -8x (4 + -8x + 4x2) + 5 = 10 Reorder the terms: 4 + 5 + -8x + 4x2 = 10 Combine like terms: 4 + 5 = 9 9 + -8x + 4x2 = 10 Solving 9 + -8x + 4x2 = 10 Solving for variable 'x'. Reorder the terms: 9 + -10 + -8x + 4x2 = 10 + -10 Combine like terms: 9 + -10 = -1 -1 + -8x + 4x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -1 + -8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -2x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -2x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -2x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -2x + x2 = 0 + 0.25 -2x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -2x + x2 = 0.25 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.25 + 1 Reorder the terms: 1 + -2x + x2 = 0.25 + 1 Combine like terms: 0.25 + 1 = 1.25 1 + -2x + x2 = 1.25 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -1) equal to 1.118033989 and -1.118033989.Subproblem 1
x + -1 = 1.118033989 Simplifying x + -1 = 1.118033989 Reorder the terms: -1 + x = 1.118033989 Solving -1 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.118033989 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.118033989 + 1 x = 1.118033989 + 1 Combine like terms: 1.118033989 + 1 = 2.118033989 x = 2.118033989 Simplifying x = 2.118033989Subproblem 2
x + -1 = -1.118033989 Simplifying x + -1 = -1.118033989 Reorder the terms: -1 + x = -1.118033989 Solving -1 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.118033989 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.118033989 + 1 x = -1.118033989 + 1 Combine like terms: -1.118033989 + 1 = -0.118033989 x = -0.118033989 Simplifying x = -0.118033989Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.118033989, -0.118033989}
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