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Simplifying 80 = x(x + -4) Reorder the terms: 80 = x(-4 + x) 80 = (-4 * x + x * x) 80 = (-4x + x2) Solving 80 = -4x + x2 Solving for variable 'x'. Reorder the terms: 80 + 4x + -1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 80 + 4x + -1x2 = 0 + x2 + -1x2 80 + 4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 80 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -80 + -4x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + -4x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + -4x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -4x + x2 = 0 + 80 -4x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 -4x + x2 = 80 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 80 + 4 Reorder the terms: 4 + -4x + x2 = 80 + 4 Combine like terms: 80 + 4 = 84 4 + -4x + x2 = 84 Factor a perfect square on the left side: (x + -2)(x + -2) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (x + -2) equal to 9.16515139 and -9.16515139.Subproblem 1
x + -2 = 9.16515139 Simplifying x + -2 = 9.16515139 Reorder the terms: -2 + x = 9.16515139 Solving -2 + x = 9.16515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 9.16515139 + 2 Combine like terms: -2 + 2 = 0 0 + x = 9.16515139 + 2 x = 9.16515139 + 2 Combine like terms: 9.16515139 + 2 = 11.16515139 x = 11.16515139 Simplifying x = 11.16515139Subproblem 2
x + -2 = -9.16515139 Simplifying x + -2 = -9.16515139 Reorder the terms: -2 + x = -9.16515139 Solving -2 + x = -9.16515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -9.16515139 + 2 Combine like terms: -2 + 2 = 0 0 + x = -9.16515139 + 2 x = -9.16515139 + 2 Combine like terms: -9.16515139 + 2 = -7.16515139 x = -7.16515139 Simplifying x = -7.16515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.16515139, -7.16515139}
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