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Simplifying 100x2 + 9 = 3x + 21 Reorder the terms: 9 + 100x2 = 3x + 21 Reorder the terms: 9 + 100x2 = 21 + 3x Solving 9 + 100x2 = 21 + 3x Solving for variable 'x'. Reorder the terms: 9 + -21 + -3x + 100x2 = 21 + 3x + -21 + -3x Combine like terms: 9 + -21 = -12 -12 + -3x + 100x2 = 21 + 3x + -21 + -3x Reorder the terms: -12 + -3x + 100x2 = 21 + -21 + 3x + -3x Combine like terms: 21 + -21 = 0 -12 + -3x + 100x2 = 0 + 3x + -3x -12 + -3x + 100x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -12 + -3x + 100x2 = 0 Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -0.12 + -0.03x + x2 = 0 Move the constant term to the right: Add '0.12' to each side of the equation. -0.12 + -0.03x + 0.12 + x2 = 0 + 0.12 Reorder the terms: -0.12 + 0.12 + -0.03x + x2 = 0 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + -0.03x + x2 = 0 + 0.12 -0.03x + x2 = 0 + 0.12 Combine like terms: 0 + 0.12 = 0.12 -0.03x + x2 = 0.12 The x term is -0.03x. Take half its coefficient (-0.015). Square it (0.000225) and add it to both sides. Add '0.000225' to each side of the equation. -0.03x + 0.000225 + x2 = 0.12 + 0.000225 Reorder the terms: 0.000225 + -0.03x + x2 = 0.12 + 0.000225 Combine like terms: 0.12 + 0.000225 = 0.120225 0.000225 + -0.03x + x2 = 0.120225 Factor a perfect square on the left side: (x + -0.015)(x + -0.015) = 0.120225 Calculate the square root of the right side: 0.346734769 Break this problem into two subproblems by setting (x + -0.015) equal to 0.346734769 and -0.346734769.Subproblem 1
x + -0.015 = 0.346734769 Simplifying x + -0.015 = 0.346734769 Reorder the terms: -0.015 + x = 0.346734769 Solving -0.015 + x = 0.346734769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.015' to each side of the equation. -0.015 + 0.015 + x = 0.346734769 + 0.015 Combine like terms: -0.015 + 0.015 = 0.000 0.000 + x = 0.346734769 + 0.015 x = 0.346734769 + 0.015 Combine like terms: 0.346734769 + 0.015 = 0.361734769 x = 0.361734769 Simplifying x = 0.361734769Subproblem 2
x + -0.015 = -0.346734769 Simplifying x + -0.015 = -0.346734769 Reorder the terms: -0.015 + x = -0.346734769 Solving -0.015 + x = -0.346734769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.015' to each side of the equation. -0.015 + 0.015 + x = -0.346734769 + 0.015 Combine like terms: -0.015 + 0.015 = 0.000 0.000 + x = -0.346734769 + 0.015 x = -0.346734769 + 0.015 Combine like terms: -0.346734769 + 0.015 = -0.331734769 x = -0.331734769 Simplifying x = -0.331734769Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.361734769, -0.331734769}
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