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Simplifying 7x2 = 8 + -3x Solving 7x2 = 8 + -3x Solving for variable 'x'. Reorder the terms: -8 + 3x + 7x2 = 8 + -3x + -8 + 3x Reorder the terms: -8 + 3x + 7x2 = 8 + -8 + -3x + 3x Combine like terms: 8 + -8 = 0 -8 + 3x + 7x2 = 0 + -3x + 3x -8 + 3x + 7x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -8 + 3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 0.4285714286x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 0.4285714286x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 0.4285714286x + x2 = 0 + 1.142857143 0.4285714286x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 0.4285714286x + x2 = 1.142857143 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = 1.142857143 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 1.142857143 + 0.04591836735 Combine like terms: 1.142857143 + 0.04591836735 = 1.18877551035 0.04591836735 + 0.4285714286x + x2 = 1.18877551035 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 1.18877551035 Calculate the square root of the right side: 1.090309823 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 1.090309823 and -1.090309823.Subproblem 1
x + 0.2142857143 = 1.090309823 Simplifying x + 0.2142857143 = 1.090309823 Reorder the terms: 0.2142857143 + x = 1.090309823 Solving 0.2142857143 + x = 1.090309823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = 1.090309823 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 1.090309823 + -0.2142857143 x = 1.090309823 + -0.2142857143 Combine like terms: 1.090309823 + -0.2142857143 = 0.8760241087 x = 0.8760241087 Simplifying x = 0.8760241087Subproblem 2
x + 0.2142857143 = -1.090309823 Simplifying x + 0.2142857143 = -1.090309823 Reorder the terms: 0.2142857143 + x = -1.090309823 Solving 0.2142857143 + x = -1.090309823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = -1.090309823 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -1.090309823 + -0.2142857143 x = -1.090309823 + -0.2142857143 Combine like terms: -1.090309823 + -0.2142857143 = -1.3045955373 x = -1.3045955373 Simplifying x = -1.3045955373Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8760241087, -1.3045955373}
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