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Simplifying (3x2 + -5x + 10) + (2x2 + 8x + -40) = 0 Reorder the terms: (10 + -5x + 3x2) + (2x2 + 8x + -40) = 0 Remove parenthesis around (10 + -5x + 3x2) 10 + -5x + 3x2 + (2x2 + 8x + -40) = 0 Reorder the terms: 10 + -5x + 3x2 + (-40 + 8x + 2x2) = 0 Remove parenthesis around (-40 + 8x + 2x2) 10 + -5x + 3x2 + -40 + 8x + 2x2 = 0 Reorder the terms: 10 + -40 + -5x + 8x + 3x2 + 2x2 = 0 Combine like terms: 10 + -40 = -30 -30 + -5x + 8x + 3x2 + 2x2 = 0 Combine like terms: -5x + 8x = 3x -30 + 3x + 3x2 + 2x2 = 0 Combine like terms: 3x2 + 2x2 = 5x2 -30 + 3x + 5x2 = 0 Solving -30 + 3x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6 + 0.6x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 0.6x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 0.6x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 0.6x + x2 = 0 + 6 0.6x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 0.6x + x2 = 6 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 6 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 6 + 0.09 Combine like terms: 6 + 0.09 = 6.09 0.09 + 0.6x + x2 = 6.09 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 6.09 Calculate the square root of the right side: 2.467792536 Break this problem into two subproblems by setting (x + 0.3) equal to 2.467792536 and -2.467792536.Subproblem 1
x + 0.3 = 2.467792536 Simplifying x + 0.3 = 2.467792536 Reorder the terms: 0.3 + x = 2.467792536 Solving 0.3 + x = 2.467792536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 2.467792536 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 2.467792536 + -0.3 x = 2.467792536 + -0.3 Combine like terms: 2.467792536 + -0.3 = 2.167792536 x = 2.167792536 Simplifying x = 2.167792536Subproblem 2
x + 0.3 = -2.467792536 Simplifying x + 0.3 = -2.467792536 Reorder the terms: 0.3 + x = -2.467792536 Solving 0.3 + x = -2.467792536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -2.467792536 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -2.467792536 + -0.3 x = -2.467792536 + -0.3 Combine like terms: -2.467792536 + -0.3 = -2.767792536 x = -2.767792536 Simplifying x = -2.767792536Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.167792536, -2.767792536}
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