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Simplifying 10x2 + -0.3x = 0.1 Reorder the terms: -0.3x + 10x2 = 0.1 Solving -0.3x + 10x2 = 0.1 Solving for variable 'x'. Reorder the terms: -0.1 + -0.3x + 10x2 = 0.1 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 -0.1 + -0.3x + 10x2 = 0.0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.01 + -0.03x + x2 = 0.0 Move the constant term to the right: Add '0.01' to each side of the equation. -0.01 + -0.03x + 0.01 + x2 = 0.0 + 0.01 Reorder the terms: -0.01 + 0.01 + -0.03x + x2 = 0.0 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.00 + -0.03x + x2 = 0.0 + 0.01 -0.03x + x2 = 0.0 + 0.01 Combine like terms: 0.0 + 0.01 = 0.01 -0.03x + x2 = 0.01 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 = 0.01 + 0.000225 Reorder the terms: 0.000225 + -0.03x + x2 = 0.01 + 0.000225 Combine like terms: 0.01 + 0.000225 = 0.010225 0.000225 + -0.03x + x2 = 0.010225 Factor a perfect square on the left side: (x + -0.015)(x + -0.015) = 0.010225 Calculate the square root of the right side: 0.101118742 Break this problem into two subproblems by setting (x + -0.015) equal to 0.101118742 and -0.101118742.Subproblem 1
x + -0.015 = 0.101118742 Simplifying x + -0.015 = 0.101118742 Reorder the terms: -0.015 + x = 0.101118742 Solving -0.015 + x = 0.101118742 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 = 0.101118742 + 0.015 Combine like terms: -0.015 + 0.015 = 0.000 0.000 + x = 0.101118742 + 0.015 x = 0.101118742 + 0.015 Combine like terms: 0.101118742 + 0.015 = 0.116118742 x = 0.116118742 Simplifying x = 0.116118742Subproblem 2
x + -0.015 = -0.101118742 Simplifying x + -0.015 = -0.101118742 Reorder the terms: -0.015 + x = -0.101118742 Solving -0.015 + x = -0.101118742 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 = -0.101118742 + 0.015 Combine like terms: -0.015 + 0.015 = 0.000 0.000 + x = -0.101118742 + 0.015 x = -0.101118742 + 0.015 Combine like terms: -0.101118742 + 0.015 = -0.086118742 x = -0.086118742 Simplifying x = -0.086118742Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.116118742, -0.086118742}
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