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Simplifying ((x)(x)) + ((x + 5)(x + 5)) = 160 Multiply x * x (x2) + ((x + 5)(x + 5)) = 160 x2 + ((x + 5)(x + 5)) = 160 Reorder the terms: x2 + ((5 + x)(x + 5)) = 160 Reorder the terms: x2 + ((5 + x)(5 + x)) = 160 Multiply (5 + x) * (5 + x) x2 + ((5(5 + x) + x(5 + x))) = 160 x2 + (((5 * 5 + x * 5) + x(5 + x))) = 160 x2 + (((25 + 5x) + x(5 + x))) = 160 x2 + ((25 + 5x + (5 * x + x * x))) = 160 x2 + ((25 + 5x + (5x + x2))) = 160 Combine like terms: 5x + 5x = 10x x2 + ((25 + 10x + x2)) = 160 x2 + (25 + 10x + x2) = 160 Remove parenthesis around (25 + 10x + x2) x2 + 25 + 10x + x2 = 160 Reorder the terms: 25 + 10x + x2 + x2 = 160 Combine like terms: x2 + x2 = 2x2 25 + 10x + 2x2 = 160 Solving 25 + 10x + 2x2 = 160 Solving for variable 'x'. Reorder the terms: 25 + -160 + 10x + 2x2 = 160 + -160 Combine like terms: 25 + -160 = -135 -135 + 10x + 2x2 = 160 + -160 Combine like terms: 160 + -160 = 0 -135 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -67.5 + 5x + x2 = 0 Move the constant term to the right: Add '67.5' to each side of the equation. -67.5 + 5x + 67.5 + x2 = 0 + 67.5 Reorder the terms: -67.5 + 67.5 + 5x + x2 = 0 + 67.5 Combine like terms: -67.5 + 67.5 = 0.0 0.0 + 5x + x2 = 0 + 67.5 5x + x2 = 0 + 67.5 Combine like terms: 0 + 67.5 = 67.5 5x + x2 = 67.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 67.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 67.5 + 6.25 Combine like terms: 67.5 + 6.25 = 73.75 6.25 + 5x + x2 = 73.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 73.75 Calculate the square root of the right side: 8.587782019 Break this problem into two subproblems by setting (x + 2.5) equal to 8.587782019 and -8.587782019.Subproblem 1
x + 2.5 = 8.587782019 Simplifying x + 2.5 = 8.587782019 Reorder the terms: 2.5 + x = 8.587782019 Solving 2.5 + x = 8.587782019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 8.587782019 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 8.587782019 + -2.5 x = 8.587782019 + -2.5 Combine like terms: 8.587782019 + -2.5 = 6.087782019 x = 6.087782019 Simplifying x = 6.087782019Subproblem 2
x + 2.5 = -8.587782019 Simplifying x + 2.5 = -8.587782019 Reorder the terms: 2.5 + x = -8.587782019 Solving 2.5 + x = -8.587782019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -8.587782019 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -8.587782019 + -2.5 x = -8.587782019 + -2.5 Combine like terms: -8.587782019 + -2.5 = -11.087782019 x = -11.087782019 Simplifying x = -11.087782019Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.087782019, -11.087782019}
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