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Simplifying 100 + 3x = x(2x + 6) Reorder the terms: 100 + 3x = x(6 + 2x) 100 + 3x = (6 * x + 2x * x) 100 + 3x = (6x + 2x2) Solving 100 + 3x = 6x + 2x2 Solving for variable 'x'. Combine like terms: 3x + -6x = -3x 100 + -3x + -2x2 = 6x + 2x2 + -6x + -2x2 Reorder the terms: 100 + -3x + -2x2 = 6x + -6x + 2x2 + -2x2 Combine like terms: 6x + -6x = 0 100 + -3x + -2x2 = 0 + 2x2 + -2x2 100 + -3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 100 + -3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -50 + 1.5x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 1.5x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 1.5x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 1.5x + x2 = 0 + 50 1.5x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 1.5x + x2 = 50 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 50 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 50 + 0.5625 Combine like terms: 50 + 0.5625 = 50.5625 0.5625 + 1.5x + x2 = 50.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 50.5625 Calculate the square root of the right side: 7.110731327 Break this problem into two subproblems by setting (x + 0.75) equal to 7.110731327 and -7.110731327.Subproblem 1
x + 0.75 = 7.110731327 Simplifying x + 0.75 = 7.110731327 Reorder the terms: 0.75 + x = 7.110731327 Solving 0.75 + x = 7.110731327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 7.110731327 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 7.110731327 + -0.75 x = 7.110731327 + -0.75 Combine like terms: 7.110731327 + -0.75 = 6.360731327 x = 6.360731327 Simplifying x = 6.360731327Subproblem 2
x + 0.75 = -7.110731327 Simplifying x + 0.75 = -7.110731327 Reorder the terms: 0.75 + x = -7.110731327 Solving 0.75 + x = -7.110731327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -7.110731327 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -7.110731327 + -0.75 x = -7.110731327 + -0.75 Combine like terms: -7.110731327 + -0.75 = -7.860731327 x = -7.860731327 Simplifying x = -7.860731327Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.360731327, -7.860731327}
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