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Simplifying 2x2 = 19x + 3 Reorder the terms: 2x2 = 3 + 19x Solving 2x2 = 3 + 19x Solving for variable 'x'. Reorder the terms: -3 + -19x + 2x2 = 3 + 19x + -3 + -19x Reorder the terms: -3 + -19x + 2x2 = 3 + -3 + 19x + -19x Combine like terms: 3 + -3 = 0 -3 + -19x + 2x2 = 0 + 19x + -19x -3 + -19x + 2x2 = 19x + -19x Combine like terms: 19x + -19x = 0 -3 + -19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -9.5x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -9.5x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -9.5x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -9.5x + x2 = 0 + 1.5 -9.5x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -9.5x + x2 = 1.5 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = 1.5 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = 1.5 + 22.5625 Combine like terms: 1.5 + 22.5625 = 24.0625 22.5625 + -9.5x + x2 = 24.0625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 24.0625 Calculate the square root of the right side: 4.905354218 Break this problem into two subproblems by setting (x + -4.75) equal to 4.905354218 and -4.905354218.Subproblem 1
x + -4.75 = 4.905354218 Simplifying x + -4.75 = 4.905354218 Reorder the terms: -4.75 + x = 4.905354218 Solving -4.75 + x = 4.905354218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 4.905354218 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 4.905354218 + 4.75 x = 4.905354218 + 4.75 Combine like terms: 4.905354218 + 4.75 = 9.655354218 x = 9.655354218 Simplifying x = 9.655354218Subproblem 2
x + -4.75 = -4.905354218 Simplifying x + -4.75 = -4.905354218 Reorder the terms: -4.75 + x = -4.905354218 Solving -4.75 + x = -4.905354218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -4.905354218 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -4.905354218 + 4.75 x = -4.905354218 + 4.75 Combine like terms: -4.905354218 + 4.75 = -0.155354218 x = -0.155354218 Simplifying x = -0.155354218Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.655354218, -0.155354218}
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