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Simplifying (x)(2x + 7) = 200 Reorder the terms: x(7 + 2x) = 200 (7 * x + 2x * x) = 200 (7x + 2x2) = 200 Solving 7x + 2x2 = 200 Solving for variable 'x'. Reorder the terms: -200 + 7x + 2x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -100 + 3.5x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 3.5x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 3.5x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 3.5x + x2 = 0 + 100 3.5x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 3.5x + x2 = 100 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 = 100 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 100 + 3.0625 Combine like terms: 100 + 3.0625 = 103.0625 3.0625 + 3.5x + x2 = 103.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 103.0625 Calculate the square root of the right side: 10.151970252 Break this problem into two subproblems by setting (x + 1.75) equal to 10.151970252 and -10.151970252.Subproblem 1
x + 1.75 = 10.151970252 Simplifying x + 1.75 = 10.151970252 Reorder the terms: 1.75 + x = 10.151970252 Solving 1.75 + x = 10.151970252 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 = 10.151970252 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 10.151970252 + -1.75 x = 10.151970252 + -1.75 Combine like terms: 10.151970252 + -1.75 = 8.401970252 x = 8.401970252 Simplifying x = 8.401970252Subproblem 2
x + 1.75 = -10.151970252 Simplifying x + 1.75 = -10.151970252 Reorder the terms: 1.75 + x = -10.151970252 Solving 1.75 + x = -10.151970252 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 = -10.151970252 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -10.151970252 + -1.75 x = -10.151970252 + -1.75 Combine like terms: -10.151970252 + -1.75 = -11.901970252 x = -11.901970252 Simplifying x = -11.901970252Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.401970252, -11.901970252}
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