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Simplifying 2x2 + -3x + 6 + 2x(x + -1) + -2 = 180 Reorder the terms: 2x2 + -3x + 6 + 2x(-1 + x) + -2 = 180 2x2 + -3x + 6 + (-1 * 2x + x * 2x) + -2 = 180 2x2 + -3x + 6 + (-2x + 2x2) + -2 = 180 Reorder the terms: 6 + -2 + -3x + -2x + 2x2 + 2x2 = 180 Combine like terms: 6 + -2 = 4 4 + -3x + -2x + 2x2 + 2x2 = 180 Combine like terms: -3x + -2x = -5x 4 + -5x + 2x2 + 2x2 = 180 Combine like terms: 2x2 + 2x2 = 4x2 4 + -5x + 4x2 = 180 Solving 4 + -5x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: 4 + -180 + -5x + 4x2 = 180 + -180 Combine like terms: 4 + -180 = -176 -176 + -5x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -176 + -5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -44 + -1.25x + x2 = 0 Move the constant term to the right: Add '44' to each side of the equation. -44 + -1.25x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + -1.25x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -1.25x + x2 = 0 + 44 -1.25x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 -1.25x + x2 = 44 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 44 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 44 + 0.390625 Combine like terms: 44 + 0.390625 = 44.390625 0.390625 + -1.25x + x2 = 44.390625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 44.390625 Calculate the square root of the right side: 6.662628986 Break this problem into two subproblems by setting (x + -0.625) equal to 6.662628986 and -6.662628986.Subproblem 1
x + -0.625 = 6.662628986 Simplifying x + -0.625 = 6.662628986 Reorder the terms: -0.625 + x = 6.662628986 Solving -0.625 + x = 6.662628986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 6.662628986 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 6.662628986 + 0.625 x = 6.662628986 + 0.625 Combine like terms: 6.662628986 + 0.625 = 7.287628986 x = 7.287628986 Simplifying x = 7.287628986Subproblem 2
x + -0.625 = -6.662628986 Simplifying x + -0.625 = -6.662628986 Reorder the terms: -0.625 + x = -6.662628986 Solving -0.625 + x = -6.662628986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -6.662628986 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -6.662628986 + 0.625 x = -6.662628986 + 0.625 Combine like terms: -6.662628986 + 0.625 = -6.037628986 x = -6.037628986 Simplifying x = -6.037628986Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.287628986, -6.037628986}
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