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Simplifying 2x2 + 8 + -4x + 3x + -6x2 + 7 = 0 Reorder the terms: 8 + 7 + -4x + 3x + 2x2 + -6x2 = 0 Combine like terms: 8 + 7 = 15 15 + -4x + 3x + 2x2 + -6x2 = 0 Combine like terms: -4x + 3x = -1x 15 + -1x + 2x2 + -6x2 = 0 Combine like terms: 2x2 + -6x2 = -4x2 15 + -1x + -4x2 = 0 Solving 15 + -1x + -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'. -3.75 + 0.25x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 0.25x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 0.25x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 0.25x + x2 = 0 + 3.75 0.25x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 0.25x + x2 = 3.75 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 3.75 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 3.75 + 0.015625 Combine like terms: 3.75 + 0.015625 = 3.765625 0.015625 + 0.25x + x2 = 3.765625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 3.765625 Calculate the square root of the right side: 1.940521837 Break this problem into two subproblems by setting (x + 0.125) equal to 1.940521837 and -1.940521837.Subproblem 1
x + 0.125 = 1.940521837 Simplifying x + 0.125 = 1.940521837 Reorder the terms: 0.125 + x = 1.940521837 Solving 0.125 + x = 1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 1.940521837 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 1.940521837 + -0.125 x = 1.940521837 + -0.125 Combine like terms: 1.940521837 + -0.125 = 1.815521837 x = 1.815521837 Simplifying x = 1.815521837Subproblem 2
x + 0.125 = -1.940521837 Simplifying x + 0.125 = -1.940521837 Reorder the terms: 0.125 + x = -1.940521837 Solving 0.125 + x = -1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -1.940521837 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -1.940521837 + -0.125 x = -1.940521837 + -0.125 Combine like terms: -1.940521837 + -0.125 = -2.065521837 x = -2.065521837 Simplifying x = -2.065521837Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.815521837, -2.065521837}
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