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Simplifying 10x2 + 3x + -24 = 0 Reorder the terms: -24 + 3x + 10x2 = 0 Solving -24 + 3x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.4 + 0.3x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 0.3x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 0.3x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 0.3x + x2 = 0 + 2.4 0.3x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 0.3x + x2 = 2.4 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 = 2.4 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 2.4 + 0.0225 Combine like terms: 2.4 + 0.0225 = 2.4225 0.0225 + 0.3x + x2 = 2.4225 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 2.4225 Calculate the square root of the right side: 1.556438242 Break this problem into two subproblems by setting (x + 0.15) equal to 1.556438242 and -1.556438242.Subproblem 1
x + 0.15 = 1.556438242 Simplifying x + 0.15 = 1.556438242 Reorder the terms: 0.15 + x = 1.556438242 Solving 0.15 + x = 1.556438242 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 = 1.556438242 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 1.556438242 + -0.15 x = 1.556438242 + -0.15 Combine like terms: 1.556438242 + -0.15 = 1.406438242 x = 1.406438242 Simplifying x = 1.406438242Subproblem 2
x + 0.15 = -1.556438242 Simplifying x + 0.15 = -1.556438242 Reorder the terms: 0.15 + x = -1.556438242 Solving 0.15 + x = -1.556438242 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 = -1.556438242 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -1.556438242 + -0.15 x = -1.556438242 + -0.15 Combine like terms: -1.556438242 + -0.15 = -1.706438242 x = -1.706438242 Simplifying x = -1.706438242Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.406438242, -1.706438242}
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