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Simplifying 10x2 + 3x + 0.6 = 1 Reorder the terms: 0.6 + 3x + 10x2 = 1 Solving 0.6 + 3x + 10x2 = 1 Solving for variable 'x'. Reorder the terms: 0.6 + -1 + 3x + 10x2 = 1 + -1 Combine like terms: 0.6 + -1 = -0.4 -0.4 + 3x + 10x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -0.4 + 3x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.04 + 0.3x + x2 = 0 Move the constant term to the right: Add '0.04' to each side of the equation. -0.04 + 0.3x + 0.04 + x2 = 0 + 0.04 Reorder the terms: -0.04 + 0.04 + 0.3x + x2 = 0 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + 0.3x + x2 = 0 + 0.04 0.3x + x2 = 0 + 0.04 Combine like terms: 0 + 0.04 = 0.04 0.3x + x2 = 0.04 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = 0.04 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 0.04 + 0.0225 Combine like terms: 0.04 + 0.0225 = 0.0625 0.0225 + 0.3x + x2 = 0.0625 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 0.0625 Calculate the square root of the right side: 0.25 Break this problem into two subproblems by setting (x + 0.15) equal to 0.25 and -0.25.Subproblem 1
x + 0.15 = 0.25 Simplifying x + 0.15 = 0.25 Reorder the terms: 0.15 + x = 0.25 Solving 0.15 + x = 0.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 0.25 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 0.25 + -0.15 x = 0.25 + -0.15 Combine like terms: 0.25 + -0.15 = 0.1 x = 0.1 Simplifying x = 0.1Subproblem 2
x + 0.15 = -0.25 Simplifying x + 0.15 = -0.25 Reorder the terms: 0.15 + x = -0.25 Solving 0.15 + x = -0.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -0.25 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -0.25 + -0.15 x = -0.25 + -0.15 Combine like terms: -0.25 + -0.15 = -0.4 x = -0.4 Simplifying x = -0.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1, -0.4}
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