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Simplifying 5x(7 + -1x) = 18 (7 * 5x + -1x * 5x) = 18 (35x + -5x2) = 18 Solving 35x + -5x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + 35x + -5x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 35x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 3.6 + -7x + x2 = 0 Move the constant term to the right: Add '-3.6' to each side of the equation. 3.6 + -7x + -3.6 + x2 = 0 + -3.6 Reorder the terms: 3.6 + -3.6 + -7x + x2 = 0 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + -7x + x2 = 0 + -3.6 -7x + x2 = 0 + -3.6 Combine like terms: 0 + -3.6 = -3.6 -7x + x2 = -3.6 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 = -3.6 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -3.6 + 12.25 Combine like terms: -3.6 + 12.25 = 8.65 12.25 + -7x + x2 = 8.65 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 8.65 Calculate the square root of the right side: 2.941088234 Break this problem into two subproblems by setting (x + -3.5) equal to 2.941088234 and -2.941088234.Subproblem 1
x + -3.5 = 2.941088234 Simplifying x + -3.5 = 2.941088234 Reorder the terms: -3.5 + x = 2.941088234 Solving -3.5 + x = 2.941088234 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 = 2.941088234 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.941088234 + 3.5 x = 2.941088234 + 3.5 Combine like terms: 2.941088234 + 3.5 = 6.441088234 x = 6.441088234 Simplifying x = 6.441088234Subproblem 2
x + -3.5 = -2.941088234 Simplifying x + -3.5 = -2.941088234 Reorder the terms: -3.5 + x = -2.941088234 Solving -3.5 + x = -2.941088234 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 = -2.941088234 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.941088234 + 3.5 x = -2.941088234 + 3.5 Combine like terms: -2.941088234 + 3.5 = 0.558911766 x = 0.558911766 Simplifying x = 0.558911766Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.441088234, 0.558911766}
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