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Simplifying x(x + -7) = 750 Reorder the terms: x(-7 + x) = 750 (-7 * x + x * x) = 750 (-7x + x2) = 750 Solving -7x + x2 = 750 Solving for variable 'x'. Reorder the terms: -750 + -7x + x2 = 750 + -750 Combine like terms: 750 + -750 = 0 -750 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '750' to each side of the equation. -750 + -7x + 750 + x2 = 0 + 750 Reorder the terms: -750 + 750 + -7x + x2 = 0 + 750 Combine like terms: -750 + 750 = 0 0 + -7x + x2 = 0 + 750 -7x + x2 = 0 + 750 Combine like terms: 0 + 750 = 750 -7x + x2 = 750 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 = 750 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 750 + 12.25 Combine like terms: 750 + 12.25 = 762.25 12.25 + -7x + x2 = 762.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 762.25 Calculate the square root of the right side: 27.608875385 Break this problem into two subproblems by setting (x + -3.5) equal to 27.608875385 and -27.608875385.Subproblem 1
x + -3.5 = 27.608875385 Simplifying x + -3.5 = 27.608875385 Reorder the terms: -3.5 + x = 27.608875385 Solving -3.5 + x = 27.608875385 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 = 27.608875385 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 27.608875385 + 3.5 x = 27.608875385 + 3.5 Combine like terms: 27.608875385 + 3.5 = 31.108875385 x = 31.108875385 Simplifying x = 31.108875385Subproblem 2
x + -3.5 = -27.608875385 Simplifying x + -3.5 = -27.608875385 Reorder the terms: -3.5 + x = -27.608875385 Solving -3.5 + x = -27.608875385 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 = -27.608875385 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -27.608875385 + 3.5 x = -27.608875385 + 3.5 Combine like terms: -27.608875385 + 3.5 = -24.108875385 x = -24.108875385 Simplifying x = -24.108875385Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.108875385, -24.108875385}
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