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Simplifying 10x2 = 19 + -3x Solving 10x2 = 19 + -3x Solving for variable 'x'. Reorder the terms: -19 + 3x + 10x2 = 19 + -3x + -19 + 3x Reorder the terms: -19 + 3x + 10x2 = 19 + -19 + -3x + 3x Combine like terms: 19 + -19 = 0 -19 + 3x + 10x2 = 0 + -3x + 3x -19 + 3x + 10x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -19 + 3x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.9 + 0.3x + x2 = 0 Move the constant term to the right: Add '1.9' to each side of the equation. -1.9 + 0.3x + 1.9 + x2 = 0 + 1.9 Reorder the terms: -1.9 + 1.9 + 0.3x + x2 = 0 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + 0.3x + x2 = 0 + 1.9 0.3x + x2 = 0 + 1.9 Combine like terms: 0 + 1.9 = 1.9 0.3x + x2 = 1.9 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 = 1.9 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 1.9 + 0.0225 Combine like terms: 1.9 + 0.0225 = 1.9225 0.0225 + 0.3x + x2 = 1.9225 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 1.9225 Calculate the square root of the right side: 1.386542462 Break this problem into two subproblems by setting (x + 0.15) equal to 1.386542462 and -1.386542462.Subproblem 1
x + 0.15 = 1.386542462 Simplifying x + 0.15 = 1.386542462 Reorder the terms: 0.15 + x = 1.386542462 Solving 0.15 + x = 1.386542462 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 = 1.386542462 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 1.386542462 + -0.15 x = 1.386542462 + -0.15 Combine like terms: 1.386542462 + -0.15 = 1.236542462 x = 1.236542462 Simplifying x = 1.236542462Subproblem 2
x + 0.15 = -1.386542462 Simplifying x + 0.15 = -1.386542462 Reorder the terms: 0.15 + x = -1.386542462 Solving 0.15 + x = -1.386542462 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 = -1.386542462 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -1.386542462 + -0.15 x = -1.386542462 + -0.15 Combine like terms: -1.386542462 + -0.15 = -1.536542462 x = -1.536542462 Simplifying x = -1.536542462Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.236542462, -1.536542462}
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