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Simplifying 7x2 + 3x + 3x + 4 = -3x + 5 Reorder the terms: 4 + 3x + 3x + 7x2 = -3x + 5 Combine like terms: 3x + 3x = 6x 4 + 6x + 7x2 = -3x + 5 Reorder the terms: 4 + 6x + 7x2 = 5 + -3x Solving 4 + 6x + 7x2 = 5 + -3x Solving for variable 'x'. Reorder the terms: 4 + -5 + 6x + 3x + 7x2 = 5 + -3x + -5 + 3x Combine like terms: 4 + -5 = -1 -1 + 6x + 3x + 7x2 = 5 + -3x + -5 + 3x Combine like terms: 6x + 3x = 9x -1 + 9x + 7x2 = 5 + -3x + -5 + 3x Reorder the terms: -1 + 9x + 7x2 = 5 + -5 + -3x + 3x Combine like terms: 5 + -5 = 0 -1 + 9x + 7x2 = 0 + -3x + 3x -1 + 9x + 7x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -1 + 9x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + 1.285714286x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + 1.285714286x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + 1.285714286x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + 1.285714286x + x2 = 0 + 0.1428571429 1.285714286x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 1.285714286x + x2 = 0.1428571429 The x term is 1.285714286x. Take half its coefficient (0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. 1.285714286x + 0.4132653063 + x2 = 0.1428571429 + 0.4132653063 Reorder the terms: 0.4132653063 + 1.285714286x + x2 = 0.1428571429 + 0.4132653063 Combine like terms: 0.1428571429 + 0.4132653063 = 0.5561224492 0.4132653063 + 1.285714286x + x2 = 0.5561224492 Factor a perfect square on the left side: (x + 0.642857143)(x + 0.642857143) = 0.5561224492 Calculate the square root of the right side: 0.745736179 Break this problem into two subproblems by setting (x + 0.642857143) equal to 0.745736179 and -0.745736179.Subproblem 1
x + 0.642857143 = 0.745736179 Simplifying x + 0.642857143 = 0.745736179 Reorder the terms: 0.642857143 + x = 0.745736179 Solving 0.642857143 + x = 0.745736179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + x = 0.745736179 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = 0.745736179 + -0.642857143 x = 0.745736179 + -0.642857143 Combine like terms: 0.745736179 + -0.642857143 = 0.102879036 x = 0.102879036 Simplifying x = 0.102879036Subproblem 2
x + 0.642857143 = -0.745736179 Simplifying x + 0.642857143 = -0.745736179 Reorder the terms: 0.642857143 + x = -0.745736179 Solving 0.642857143 + x = -0.745736179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + x = -0.745736179 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = -0.745736179 + -0.642857143 x = -0.745736179 + -0.642857143 Combine like terms: -0.745736179 + -0.642857143 = -1.388593322 x = -1.388593322 Simplifying x = -1.388593322Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.102879036, -1.388593322}
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