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Simplifying 0.120x2 + 0.12 + 0.03 = 3 + -1x Reorder the terms: 0.12 + 0.03 + 0.120x2 = 3 + -1x Combine like terms: 0.12 + 0.03 = 0.15 0.15 + 0.120x2 = 3 + -1x Solving 0.15 + 0.120x2 = 3 + -1x Solving for variable 'x'. Reorder the terms: 0.15 + -3 + x + 0.120x2 = 3 + -1x + -3 + x Combine like terms: 0.15 + -3 = -2.85 -2.85 + x + 0.120x2 = 3 + -1x + -3 + x Reorder the terms: -2.85 + x + 0.120x2 = 3 + -3 + -1x + x Combine like terms: 3 + -3 = 0 -2.85 + x + 0.120x2 = 0 + -1x + x -2.85 + x + 0.120x2 = -1x + x Combine like terms: -1x + x = 0 -2.85 + x + 0.120x2 = 0 Begin completing the square. Divide all terms by 0.120 the coefficient of the squared term: Divide each side by '0.120'. -23.75 + 8.333333333x + x2 = 0 Move the constant term to the right: Add '23.75' to each side of the equation. -23.75 + 8.333333333x + 23.75 + x2 = 0 + 23.75 Reorder the terms: -23.75 + 23.75 + 8.333333333x + x2 = 0 + 23.75 Combine like terms: -23.75 + 23.75 = 0.00 0.00 + 8.333333333x + x2 = 0 + 23.75 8.333333333x + x2 = 0 + 23.75 Combine like terms: 0 + 23.75 = 23.75 8.333333333x + x2 = 23.75 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 8.333333333x + 0.25 + x2 = 23.75 + 0.25 Reorder the terms: 0.25 + 8.333333333x + x2 = 23.75 + 0.25 Combine like terms: 23.75 + 0.25 = 24 0.25 + 8.333333333x + x2 = 24 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + 0.5) equal to 4.898979486 and -4.898979486.Subproblem 1
x + 0.5 = 4.898979486 Simplifying x + 0.5 = 4.898979486 Reorder the terms: 0.5 + x = 4.898979486 Solving 0.5 + x = 4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.898979486 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.898979486 + -0.5 x = 4.898979486 + -0.5 Combine like terms: 4.898979486 + -0.5 = 4.398979486 x = 4.398979486 Simplifying x = 4.398979486Subproblem 2
x + 0.5 = -4.898979486 Simplifying x + 0.5 = -4.898979486 Reorder the terms: 0.5 + x = -4.898979486 Solving 0.5 + x = -4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.898979486 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.898979486 + -0.5 x = -4.898979486 + -0.5 Combine like terms: -4.898979486 + -0.5 = -5.398979486 x = -5.398979486 Simplifying x = -5.398979486Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.398979486, -5.398979486}
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