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Simplifying 2x2 = 19x + 4 Reorder the terms: 2x2 = 4 + 19x Solving 2x2 = 4 + 19x Solving for variable 'x'. Reorder the terms: -4 + -19x + 2x2 = 4 + 19x + -4 + -19x Reorder the terms: -4 + -19x + 2x2 = 4 + -4 + 19x + -19x Combine like terms: 4 + -4 = 0 -4 + -19x + 2x2 = 0 + 19x + -19x -4 + -19x + 2x2 = 19x + -19x Combine like terms: 19x + -19x = 0 -4 + -19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + -9.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -9.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -9.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -9.5x + x2 = 0 + 2 -9.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -9.5x + x2 = 2 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 = 2 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = 2 + 22.5625 Combine like terms: 2 + 22.5625 = 24.5625 22.5625 + -9.5x + x2 = 24.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 24.5625 Calculate the square root of the right side: 4.9560569 Break this problem into two subproblems by setting (x + -4.75) equal to 4.9560569 and -4.9560569.Subproblem 1
x + -4.75 = 4.9560569 Simplifying x + -4.75 = 4.9560569 Reorder the terms: -4.75 + x = 4.9560569 Solving -4.75 + x = 4.9560569 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 = 4.9560569 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 4.9560569 + 4.75 x = 4.9560569 + 4.75 Combine like terms: 4.9560569 + 4.75 = 9.7060569 x = 9.7060569 Simplifying x = 9.7060569Subproblem 2
x + -4.75 = -4.9560569 Simplifying x + -4.75 = -4.9560569 Reorder the terms: -4.75 + x = -4.9560569 Solving -4.75 + x = -4.9560569 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 = -4.9560569 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -4.9560569 + 4.75 x = -4.9560569 + 4.75 Combine like terms: -4.9560569 + 4.75 = -0.2060569 x = -0.2060569 Simplifying x = -0.2060569Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.7060569, -0.2060569}
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