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Simplifying x(2x + 7) = 87 Reorder the terms: x(7 + 2x) = 87 (7 * x + 2x * x) = 87 (7x + 2x2) = 87 Solving 7x + 2x2 = 87 Solving for variable 'x'. Reorder the terms: -87 + 7x + 2x2 = 87 + -87 Combine like terms: 87 + -87 = 0 -87 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -43.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '43.5' to each side of the equation. -43.5 + 3.5x + 43.5 + x2 = 0 + 43.5 Reorder the terms: -43.5 + 43.5 + 3.5x + x2 = 0 + 43.5 Combine like terms: -43.5 + 43.5 = 0.0 0.0 + 3.5x + x2 = 0 + 43.5 3.5x + x2 = 0 + 43.5 Combine like terms: 0 + 43.5 = 43.5 3.5x + x2 = 43.5 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 43.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 43.5 + 3.0625 Combine like terms: 43.5 + 3.0625 = 46.5625 3.0625 + 3.5x + x2 = 46.5625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 46.5625 Calculate the square root of the right side: 6.823672032 Break this problem into two subproblems by setting (x + 1.75) equal to 6.823672032 and -6.823672032.Subproblem 1
x + 1.75 = 6.823672032 Simplifying x + 1.75 = 6.823672032 Reorder the terms: 1.75 + x = 6.823672032 Solving 1.75 + x = 6.823672032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 6.823672032 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 6.823672032 + -1.75 x = 6.823672032 + -1.75 Combine like terms: 6.823672032 + -1.75 = 5.073672032 x = 5.073672032 Simplifying x = 5.073672032Subproblem 2
x + 1.75 = -6.823672032 Simplifying x + 1.75 = -6.823672032 Reorder the terms: 1.75 + x = -6.823672032 Solving 1.75 + x = -6.823672032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -6.823672032 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -6.823672032 + -1.75 x = -6.823672032 + -1.75 Combine like terms: -6.823672032 + -1.75 = -8.573672032 x = -8.573672032 Simplifying x = -8.573672032Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.073672032, -8.573672032}
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