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Simplifying x2 + 6x + 9 = 100x Reorder the terms: 9 + 6x + x2 = 100x Solving 9 + 6x + x2 = 100x Solving for variable 'x'. Reorder the terms: 9 + 6x + -100x + x2 = 100x + -100x Combine like terms: 6x + -100x = -94x 9 + -94x + x2 = 100x + -100x Combine like terms: 100x + -100x = 0 9 + -94x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -94x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -94x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -94x + x2 = 0 + -9 -94x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -94x + x2 = -9 The x term is -94x. Take half its coefficient (-47). Square it (2209) and add it to both sides. Add '2209' to each side of the equation. -94x + 2209 + x2 = -9 + 2209 Reorder the terms: 2209 + -94x + x2 = -9 + 2209 Combine like terms: -9 + 2209 = 2200 2209 + -94x + x2 = 2200 Factor a perfect square on the left side: (x + -47)(x + -47) = 2200 Calculate the square root of the right side: 46.904157598 Break this problem into two subproblems by setting (x + -47) equal to 46.904157598 and -46.904157598.Subproblem 1
x + -47 = 46.904157598 Simplifying x + -47 = 46.904157598 Reorder the terms: -47 + x = 46.904157598 Solving -47 + x = 46.904157598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '47' to each side of the equation. -47 + 47 + x = 46.904157598 + 47 Combine like terms: -47 + 47 = 0 0 + x = 46.904157598 + 47 x = 46.904157598 + 47 Combine like terms: 46.904157598 + 47 = 93.904157598 x = 93.904157598 Simplifying x = 93.904157598Subproblem 2
x + -47 = -46.904157598 Simplifying x + -47 = -46.904157598 Reorder the terms: -47 + x = -46.904157598 Solving -47 + x = -46.904157598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '47' to each side of the equation. -47 + 47 + x = -46.904157598 + 47 Combine like terms: -47 + 47 = 0 0 + x = -46.904157598 + 47 x = -46.904157598 + 47 Combine like terms: -46.904157598 + 47 = 0.095842402 x = 0.095842402 Simplifying x = 0.095842402Solution
The solution to the problem is based on the solutions from the subproblems. x = {93.904157598, 0.095842402}
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