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Simplifying 7x2 + -37x + -36 = 0 Reorder the terms: -36 + -37x + 7x2 = 0 Solving -36 + -37x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.142857143 + -5.285714286x + x2 = 0 Move the constant term to the right: Add '5.142857143' to each side of the equation. -5.142857143 + -5.285714286x + 5.142857143 + x2 = 0 + 5.142857143 Reorder the terms: -5.142857143 + 5.142857143 + -5.285714286x + x2 = 0 + 5.142857143 Combine like terms: -5.142857143 + 5.142857143 = 0.000000000 0.000000000 + -5.285714286x + x2 = 0 + 5.142857143 -5.285714286x + x2 = 0 + 5.142857143 Combine like terms: 0 + 5.142857143 = 5.142857143 -5.285714286x + x2 = 5.142857143 The x term is -5.285714286x. Take half its coefficient (-2.642857143). Square it (6.984693878) and add it to both sides. Add '6.984693878' to each side of the equation. -5.285714286x + 6.984693878 + x2 = 5.142857143 + 6.984693878 Reorder the terms: 6.984693878 + -5.285714286x + x2 = 5.142857143 + 6.984693878 Combine like terms: 5.142857143 + 6.984693878 = 12.127551021 6.984693878 + -5.285714286x + x2 = 12.127551021 Factor a perfect square on the left side: (x + -2.642857143)(x + -2.642857143) = 12.127551021 Calculate the square root of the right side: 3.482463355 Break this problem into two subproblems by setting (x + -2.642857143) equal to 3.482463355 and -3.482463355.Subproblem 1
x + -2.642857143 = 3.482463355 Simplifying x + -2.642857143 = 3.482463355 Reorder the terms: -2.642857143 + x = 3.482463355 Solving -2.642857143 + x = 3.482463355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.642857143' to each side of the equation. -2.642857143 + 2.642857143 + x = 3.482463355 + 2.642857143 Combine like terms: -2.642857143 + 2.642857143 = 0.000000000 0.000000000 + x = 3.482463355 + 2.642857143 x = 3.482463355 + 2.642857143 Combine like terms: 3.482463355 + 2.642857143 = 6.125320498 x = 6.125320498 Simplifying x = 6.125320498Subproblem 2
x + -2.642857143 = -3.482463355 Simplifying x + -2.642857143 = -3.482463355 Reorder the terms: -2.642857143 + x = -3.482463355 Solving -2.642857143 + x = -3.482463355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.642857143' to each side of the equation. -2.642857143 + 2.642857143 + x = -3.482463355 + 2.642857143 Combine like terms: -2.642857143 + 2.642857143 = 0.000000000 0.000000000 + x = -3.482463355 + 2.642857143 x = -3.482463355 + 2.642857143 Combine like terms: -3.482463355 + 2.642857143 = -0.839606212 x = -0.839606212 Simplifying x = -0.839606212Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.125320498, -0.839606212}
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