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Simplifying x(x + -7) = 1100 Reorder the terms: x(-7 + x) = 1100 (-7 * x + x * x) = 1100 (-7x + x2) = 1100 Solving -7x + x2 = 1100 Solving for variable 'x'. Reorder the terms: -1100 + -7x + x2 = 1100 + -1100 Combine like terms: 1100 + -1100 = 0 -1100 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1100' to each side of the equation. -1100 + -7x + 1100 + x2 = 0 + 1100 Reorder the terms: -1100 + 1100 + -7x + x2 = 0 + 1100 Combine like terms: -1100 + 1100 = 0 0 + -7x + x2 = 0 + 1100 -7x + x2 = 0 + 1100 Combine like terms: 0 + 1100 = 1100 -7x + x2 = 1100 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 1100 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 1100 + 12.25 Combine like terms: 1100 + 12.25 = 1112.25 12.25 + -7x + x2 = 1112.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 1112.25 Calculate the square root of the right side: 33.350412291 Break this problem into two subproblems by setting (x + -3.5) equal to 33.350412291 and -33.350412291.Subproblem 1
x + -3.5 = 33.350412291 Simplifying x + -3.5 = 33.350412291 Reorder the terms: -3.5 + x = 33.350412291 Solving -3.5 + x = 33.350412291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 33.350412291 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 33.350412291 + 3.5 x = 33.350412291 + 3.5 Combine like terms: 33.350412291 + 3.5 = 36.850412291 x = 36.850412291 Simplifying x = 36.850412291Subproblem 2
x + -3.5 = -33.350412291 Simplifying x + -3.5 = -33.350412291 Reorder the terms: -3.5 + x = -33.350412291 Solving -3.5 + x = -33.350412291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -33.350412291 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -33.350412291 + 3.5 x = -33.350412291 + 3.5 Combine like terms: -33.350412291 + 3.5 = -29.850412291 x = -29.850412291 Simplifying x = -29.850412291Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.850412291, -29.850412291}
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