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Simplifying 5x2 + 4x + -7x2 + 11 + 8x = 0 Reorder the terms: 11 + 4x + 8x + 5x2 + -7x2 = 0 Combine like terms: 4x + 8x = 12x 11 + 12x + 5x2 + -7x2 = 0 Combine like terms: 5x2 + -7x2 = -2x2 11 + 12x + -2x2 = 0 Solving 11 + 12x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -5.5 + -6x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -6x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -6x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -6x + x2 = 0 + 5.5 -6x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -6x + x2 = 5.5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 5.5 + 9 Reorder the terms: 9 + -6x + x2 = 5.5 + 9 Combine like terms: 5.5 + 9 = 14.5 9 + -6x + x2 = 14.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 14.5 Calculate the square root of the right side: 3.807886553 Break this problem into two subproblems by setting (x + -3) equal to 3.807886553 and -3.807886553.Subproblem 1
x + -3 = 3.807886553 Simplifying x + -3 = 3.807886553 Reorder the terms: -3 + x = 3.807886553 Solving -3 + x = 3.807886553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.807886553 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.807886553 + 3 x = 3.807886553 + 3 Combine like terms: 3.807886553 + 3 = 6.807886553 x = 6.807886553 Simplifying x = 6.807886553Subproblem 2
x + -3 = -3.807886553 Simplifying x + -3 = -3.807886553 Reorder the terms: -3 + x = -3.807886553 Solving -3 + x = -3.807886553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.807886553 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.807886553 + 3 x = -3.807886553 + 3 Combine like terms: -3.807886553 + 3 = -0.807886553 x = -0.807886553 Simplifying x = -0.807886553Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.807886553, -0.807886553}
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