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Simplifying (6x2 + -3x + -2) + -1(5x + -4x2 + 9) = 0 Reorder the terms: (-2 + -3x + 6x2) + -1(5x + -4x2 + 9) = 0 Remove parenthesis around (-2 + -3x + 6x2) -2 + -3x + 6x2 + -1(5x + -4x2 + 9) = 0 Reorder the terms: -2 + -3x + 6x2 + -1(9 + 5x + -4x2) = 0 -2 + -3x + 6x2 + (9 * -1 + 5x * -1 + -4x2 * -1) = 0 -2 + -3x + 6x2 + (-9 + -5x + 4x2) = 0 Reorder the terms: -2 + -9 + -3x + -5x + 6x2 + 4x2 = 0 Combine like terms: -2 + -9 = -11 -11 + -3x + -5x + 6x2 + 4x2 = 0 Combine like terms: -3x + -5x = -8x -11 + -8x + 6x2 + 4x2 = 0 Combine like terms: 6x2 + 4x2 = 10x2 -11 + -8x + 10x2 = 0 Solving -11 + -8x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.1 + -0.8x + x2 = 0.0 Move the constant term to the right: Add '1.1' to each side of the equation. -1.1 + -0.8x + 1.1 + x2 = 0.0 + 1.1 Reorder the terms: -1.1 + 1.1 + -0.8x + x2 = 0.0 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + -0.8x + x2 = 0.0 + 1.1 -0.8x + x2 = 0.0 + 1.1 Combine like terms: 0.0 + 1.1 = 1.1 -0.8x + x2 = 1.1 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 1.1 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 1.1 + 0.16 Combine like terms: 1.1 + 0.16 = 1.26 0.16 + -0.8x + x2 = 1.26 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 1.26 Calculate the square root of the right side: 1.122497216 Break this problem into two subproblems by setting (x + -0.4) equal to 1.122497216 and -1.122497216.Subproblem 1
x + -0.4 = 1.122497216 Simplifying x + -0.4 = 1.122497216 Reorder the terms: -0.4 + x = 1.122497216 Solving -0.4 + x = 1.122497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 1.122497216 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.122497216 + 0.4 x = 1.122497216 + 0.4 Combine like terms: 1.122497216 + 0.4 = 1.522497216 x = 1.522497216 Simplifying x = 1.522497216Subproblem 2
x + -0.4 = -1.122497216 Simplifying x + -0.4 = -1.122497216 Reorder the terms: -0.4 + x = -1.122497216 Solving -0.4 + x = -1.122497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -1.122497216 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.122497216 + 0.4 x = -1.122497216 + 0.4 Combine like terms: -1.122497216 + 0.4 = -0.722497216 x = -0.722497216 Simplifying x = -0.722497216Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.522497216, -0.722497216}
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