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Simplifying 0.2x + -30 + x(5 + x) = 100000 0.2x + -30 + (5 * x + x * x) = 100000 0.2x + -30 + (5x + x2) = 100000 Reorder the terms: -30 + 0.2x + 5x + x2 = 100000 Combine like terms: 0.2x + 5x = 5.2x -30 + 5.2x + x2 = 100000 Solving -30 + 5.2x + x2 = 100000 Solving for variable 'x'. Reorder the terms: -30 + -100000 + 5.2x + x2 = 100000 + -100000 Combine like terms: -30 + -100000 = -100030 -100030 + 5.2x + x2 = 100000 + -100000 Combine like terms: 100000 + -100000 = 0 -100030 + 5.2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100030' to each side of the equation. -100030 + 5.2x + 100030 + x2 = 0 + 100030 Reorder the terms: -100030 + 100030 + 5.2x + x2 = 0 + 100030 Combine like terms: -100030 + 100030 = 0 0 + 5.2x + x2 = 0 + 100030 5.2x + x2 = 0 + 100030 Combine like terms: 0 + 100030 = 100030 5.2x + x2 = 100030 The x term is 5.2x. Take half its coefficient (2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. 5.2x + 6.76 + x2 = 100030 + 6.76 Reorder the terms: 6.76 + 5.2x + x2 = 100030 + 6.76 Combine like terms: 100030 + 6.76 = 100036.76 6.76 + 5.2x + x2 = 100036.76 Factor a perfect square on the left side: (x + 2.6)(x + 2.6) = 100036.76 Calculate the square root of the right side: 316.28588334 Break this problem into two subproblems by setting (x + 2.6) equal to 316.28588334 and -316.28588334.Subproblem 1
x + 2.6 = 316.28588334 Simplifying x + 2.6 = 316.28588334 Reorder the terms: 2.6 + x = 316.28588334 Solving 2.6 + x = 316.28588334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = 316.28588334 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = 316.28588334 + -2.6 x = 316.28588334 + -2.6 Combine like terms: 316.28588334 + -2.6 = 313.68588334 x = 313.68588334 Simplifying x = 313.68588334Subproblem 2
x + 2.6 = -316.28588334 Simplifying x + 2.6 = -316.28588334 Reorder the terms: 2.6 + x = -316.28588334 Solving 2.6 + x = -316.28588334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = -316.28588334 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = -316.28588334 + -2.6 x = -316.28588334 + -2.6 Combine like terms: -316.28588334 + -2.6 = -318.88588334 x = -318.88588334 Simplifying x = -318.88588334Solution
The solution to the problem is based on the solutions from the subproblems. x = {313.68588334, -318.88588334}
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