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Simplifying 2x * 2x + 4x + -37 = 0 Reorder the terms for easier multiplication: 2 * 2x * x + 4x + -37 = 0 Multiply 2 * 2 4x * x + 4x + -37 = 0 Multiply x * x 4x2 + 4x + -37 = 0 Reorder the terms: -37 + 4x + 4x2 = 0 Solving -37 + 4x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9.25 + x + x2 = 0 Move the constant term to the right: Add '9.25' to each side of the equation. -9.25 + x + 9.25 + x2 = 0 + 9.25 Reorder the terms: -9.25 + 9.25 + x + x2 = 0 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + x + x2 = 0 + 9.25 x + x2 = 0 + 9.25 Combine like terms: 0 + 9.25 = 9.25 x + x2 = 9.25 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 9.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 9.25 + 0.25 Combine like terms: 9.25 + 0.25 = 9.5 1.25 + x2 = 9.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (x + 0.5) equal to 3.082207001 and -3.082207001.Subproblem 1
x + 0.5 = 3.082207001 Simplifying x + 0.5 = 3.082207001 Reorder the terms: 0.5 + x = 3.082207001 Solving 0.5 + x = 3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.082207001 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.082207001 + -0.5 x = 3.082207001 + -0.5 Combine like terms: 3.082207001 + -0.5 = 2.582207001 x = 2.582207001 Simplifying x = 2.582207001Subproblem 2
x + 0.5 = -3.082207001 Simplifying x + 0.5 = -3.082207001 Reorder the terms: 0.5 + x = -3.082207001 Solving 0.5 + x = -3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.082207001 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.082207001 + -0.5 x = -3.082207001 + -0.5 Combine like terms: -3.082207001 + -0.5 = -3.582207001 x = -3.582207001 Simplifying x = -3.582207001Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.582207001, -3.582207001}
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