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Simplifying 2x2 = 19 + -3x Solving 2x2 = 19 + -3x Solving for variable 'x'. Reorder the terms: -19 + 3x + 2x2 = 19 + -3x + -19 + 3x Reorder the terms: -19 + 3x + 2x2 = 19 + -19 + -3x + 3x Combine like terms: 19 + -19 = 0 -19 + 3x + 2x2 = 0 + -3x + 3x -19 + 3x + 2x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -19 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + 1.5x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + 1.5x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + 1.5x + x2 = 0 + 9.5 1.5x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 1.5x + x2 = 9.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 9.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 9.5 + 0.5625 Combine like terms: 9.5 + 0.5625 = 10.0625 0.5625 + 1.5x + x2 = 10.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (x + 0.75) equal to 3.172144385 and -3.172144385.Subproblem 1
x + 0.75 = 3.172144385 Simplifying x + 0.75 = 3.172144385 Reorder the terms: 0.75 + x = 3.172144385 Solving 0.75 + x = 3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 3.172144385 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 3.172144385 + -0.75 x = 3.172144385 + -0.75 Combine like terms: 3.172144385 + -0.75 = 2.422144385 x = 2.422144385 Simplifying x = 2.422144385Subproblem 2
x + 0.75 = -3.172144385 Simplifying x + 0.75 = -3.172144385 Reorder the terms: 0.75 + x = -3.172144385 Solving 0.75 + x = -3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -3.172144385 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -3.172144385 + -0.75 x = -3.172144385 + -0.75 Combine like terms: -3.172144385 + -0.75 = -3.922144385 x = -3.922144385 Simplifying x = -3.922144385Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.422144385, -3.922144385}
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