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Simplifying 7 + -1(2x + -2)(5 + x) = 2x2 Reorder the terms: 7 + -1(-2 + 2x)(5 + x) = 2x2 Multiply (-2 + 2x) * (5 + x) 7 + -1(-2(5 + x) + 2x * (5 + x)) = 2x2 7 + -1((5 * -2 + x * -2) + 2x * (5 + x)) = 2x2 7 + -1((-10 + -2x) + 2x * (5 + x)) = 2x2 7 + -1(-10 + -2x + (5 * 2x + x * 2x)) = 2x2 7 + -1(-10 + -2x + (10x + 2x2)) = 2x2 Combine like terms: -2x + 10x = 8x 7 + -1(-10 + 8x + 2x2) = 2x2 7 + (-10 * -1 + 8x * -1 + 2x2 * -1) = 2x2 7 + (10 + -8x + -2x2) = 2x2 Combine like terms: 7 + 10 = 17 17 + -8x + -2x2 = 2x2 Solving 17 + -8x + -2x2 = 2x2 Solving for variable 'x'. Combine like terms: -2x2 + -2x2 = -4x2 17 + -8x + -4x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 17 + -8x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -4.25 + 2x + x2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + 2x + 4.25 + x2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + 2x + x2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + 2x + x2 = 0 + 4.25 2x + x2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 2x + x2 = 4.25 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 = 4.25 + 1 Reorder the terms: 1 + 2x + x2 = 4.25 + 1 Combine like terms: 4.25 + 1 = 5.25 1 + 2x + x2 = 5.25 Factor a perfect square on the left side: (x + 1)(x + 1) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + 1) equal to 2.291287847 and -2.291287847.Subproblem 1
x + 1 = 2.291287847 Simplifying x + 1 = 2.291287847 Reorder the terms: 1 + x = 2.291287847 Solving 1 + x = 2.291287847 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 = 2.291287847 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.291287847 + -1 x = 2.291287847 + -1 Combine like terms: 2.291287847 + -1 = 1.291287847 x = 1.291287847 Simplifying x = 1.291287847Subproblem 2
x + 1 = -2.291287847 Simplifying x + 1 = -2.291287847 Reorder the terms: 1 + x = -2.291287847 Solving 1 + x = -2.291287847 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 = -2.291287847 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.291287847 + -1 x = -2.291287847 + -1 Combine like terms: -2.291287847 + -1 = -3.291287847 x = -3.291287847 Simplifying x = -3.291287847Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.291287847, -3.291287847}
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