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Simplifying (x + 4)(2x + -7) = 18 Reorder the terms: (4 + x)(2x + -7) = 18 Reorder the terms: (4 + x)(-7 + 2x) = 18 Multiply (4 + x) * (-7 + 2x) (4(-7 + 2x) + x(-7 + 2x)) = 18 ((-7 * 4 + 2x * 4) + x(-7 + 2x)) = 18 ((-28 + 8x) + x(-7 + 2x)) = 18 (-28 + 8x + (-7 * x + 2x * x)) = 18 (-28 + 8x + (-7x + 2x2)) = 18 Combine like terms: 8x + -7x = 1x (-28 + 1x + 2x2) = 18 Solving -28 + 1x + 2x2 = 18 Solving for variable 'x'. Reorder the terms: -28 + -18 + 1x + 2x2 = 18 + -18 Combine like terms: -28 + -18 = -46 -46 + 1x + 2x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -46 + 1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -23 + 0.5x + x2 = 0 Move the constant term to the right: Add '23' to each side of the equation. -23 + 0.5x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + 0.5x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 0.5x + x2 = 0 + 23 0.5x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 0.5x + x2 = 23 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 23 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 23 + 0.0625 Combine like terms: 23 + 0.0625 = 23.0625 0.0625 + 0.5x + x2 = 23.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 23.0625 Calculate the square root of the right side: 4.802343178 Break this problem into two subproblems by setting (x + 0.25) equal to 4.802343178 and -4.802343178.Subproblem 1
x + 0.25 = 4.802343178 Simplifying x + 0.25 = 4.802343178 Reorder the terms: 0.25 + x = 4.802343178 Solving 0.25 + x = 4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 4.802343178 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 4.802343178 + -0.25 x = 4.802343178 + -0.25 Combine like terms: 4.802343178 + -0.25 = 4.552343178 x = 4.552343178 Simplifying x = 4.552343178Subproblem 2
x + 0.25 = -4.802343178 Simplifying x + 0.25 = -4.802343178 Reorder the terms: 0.25 + x = -4.802343178 Solving 0.25 + x = -4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -4.802343178 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -4.802343178 + -0.25 x = -4.802343178 + -0.25 Combine like terms: -4.802343178 + -0.25 = -5.052343178 x = -5.052343178 Simplifying x = -5.052343178Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.552343178, -5.052343178}
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